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A dynamical CP source for CKM, PMNS and Leptogenesis Yang-Hwan, Ahn (KIAS) Collaboration with Seungwon Baek It will appear in arXiv soooon PPP10 2013 @ CYCU, Taiwan, 30 May
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A dynamical CP source for
CKM PMNS and Leptogenesis
Yang-Hwan Ahn (KIAS)
Collaboration with Seungwon Baek
It will appear in arXiv soooon
PPP10 2013 CYCU Taiwan 30 May
Contents
Motivation Why SCPV
Present knowledges on quark and lepton sectors
In a economical and theoretical way in order to understand the present
data for quarks and leptons as well as to predict CP violation in PMNS and
a successful leptogenesis
We propose a simple model for SCPV based on A4 flavor
symmetry for quarks and leptons in a seesaw framework
Low-energy phenomenology of quarks and leptons
and Leptogenesis
2013-05-30
Why SCPV
Spontaneous CP violation Spontaneous CP violation (SCPV) occurs when CP is a gooood symmetry of the
original Lagrangian but after SSB no CP symmetry remains (1973 TD Lee)
Renormalizable gauge theories are based on the SSB mechanism and it is
natural to have the SCPV as an integral part of that mechanism
In the SM it is not possible to have spontaneous CP violation and to violate CP
explicitly in the Higgs sector
The origin of the observed CKM CP violation
Explicitly violated by Yukawa couplings
SCPV in the Higgs potential (rarr More than 2)
We are in need of a fundamental understanding of the origin of CP violation
CP violation is one of the crucial ingredients necessary to generate
the observed Matter-antimatter asymmetry of the Universe as well as
to explain low energy CP violation
It is not enough for the SM CP violation to lead to the observed BAU
Non-zero 13 in neutrino oscillation Exps CP violations in the lepton sector
can strengthen our belief in the BAU originated from leptogenesis scenario
QCD θ problem Peccei-Quinn CP is violated softly or spontaneously
2013-05-30
Present Knowledges on Quark and Lepton sectors
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Cosmological limit (including WMAP 3-years result)
upper bound on neutrino masses
(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)
Starting to disfavor the degenerate spectrum of neutrinos
BAU Astrophys J Suppl 192 (2011) 18
the most plausiblehellipBUT difficult to direct test
at seesaw scale18 parameters at low energy 9 observables
2013-05-30
B 10of baryons(N )62
of photons1
)0
(NB
Where Do we Stand There are empirical fermion mass hierarchies in the charged leptons up- and down-type
quark sectors calculated from the measured values (PDG)
mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21
Quark mixing angles
2013-05-30
Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data
one can assume a flavor symmetry which may reduce the unknown parameters
Unless flavor symmetries are assumed particle masses and mixings are generally
undetermined in gauge theory
A4 Trsquo S4 S3helliphellip Discrete amp Non-Abelian
global
spontaneously broken at high-energy
broken by a set of scalar fields which transform only under the flavor sym
Symmetry
Breaking
2013-05-30
A4 Symmetry (Smallest group for three-families) A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects 42=12 elements Generator S and T with the relations S2=T3=(ST)3=I S2=I Z2 symmetry T3=I Z3 symmetry Elements I S T ST TS T2 ST2 STS TST T2S TST2 T2ST There are 4 irreducible representation 1 1 1 3
Ma amp Rajasekaran
Why A4
A4 is the smallest discrete group that has 3-dimensional irreducible representation
A4 flavor symmetry can give a micro- symmetric pattern
for experimental data
A4 flavor symmetry can provide SCPV
2013-05-30
1
3
4
2
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Contents
Motivation Why SCPV
Present knowledges on quark and lepton sectors
In a economical and theoretical way in order to understand the present
data for quarks and leptons as well as to predict CP violation in PMNS and
a successful leptogenesis
We propose a simple model for SCPV based on A4 flavor
symmetry for quarks and leptons in a seesaw framework
Low-energy phenomenology of quarks and leptons
and Leptogenesis
2013-05-30
Why SCPV
Spontaneous CP violation Spontaneous CP violation (SCPV) occurs when CP is a gooood symmetry of the
original Lagrangian but after SSB no CP symmetry remains (1973 TD Lee)
Renormalizable gauge theories are based on the SSB mechanism and it is
natural to have the SCPV as an integral part of that mechanism
In the SM it is not possible to have spontaneous CP violation and to violate CP
explicitly in the Higgs sector
The origin of the observed CKM CP violation
Explicitly violated by Yukawa couplings
SCPV in the Higgs potential (rarr More than 2)
We are in need of a fundamental understanding of the origin of CP violation
CP violation is one of the crucial ingredients necessary to generate
the observed Matter-antimatter asymmetry of the Universe as well as
to explain low energy CP violation
It is not enough for the SM CP violation to lead to the observed BAU
Non-zero 13 in neutrino oscillation Exps CP violations in the lepton sector
can strengthen our belief in the BAU originated from leptogenesis scenario
QCD θ problem Peccei-Quinn CP is violated softly or spontaneously
2013-05-30
Present Knowledges on Quark and Lepton sectors
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Cosmological limit (including WMAP 3-years result)
upper bound on neutrino masses
(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)
Starting to disfavor the degenerate spectrum of neutrinos
BAU Astrophys J Suppl 192 (2011) 18
the most plausiblehellipBUT difficult to direct test
at seesaw scale18 parameters at low energy 9 observables
2013-05-30
B 10of baryons(N )62
of photons1
)0
(NB
Where Do we Stand There are empirical fermion mass hierarchies in the charged leptons up- and down-type
quark sectors calculated from the measured values (PDG)
mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21
Quark mixing angles
2013-05-30
Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data
one can assume a flavor symmetry which may reduce the unknown parameters
Unless flavor symmetries are assumed particle masses and mixings are generally
undetermined in gauge theory
A4 Trsquo S4 S3helliphellip Discrete amp Non-Abelian
global
spontaneously broken at high-energy
broken by a set of scalar fields which transform only under the flavor sym
Symmetry
Breaking
2013-05-30
A4 Symmetry (Smallest group for three-families) A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects 42=12 elements Generator S and T with the relations S2=T3=(ST)3=I S2=I Z2 symmetry T3=I Z3 symmetry Elements I S T ST TS T2 ST2 STS TST T2S TST2 T2ST There are 4 irreducible representation 1 1 1 3
Ma amp Rajasekaran
Why A4
A4 is the smallest discrete group that has 3-dimensional irreducible representation
A4 flavor symmetry can give a micro- symmetric pattern
for experimental data
A4 flavor symmetry can provide SCPV
2013-05-30
1
3
4
2
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Why SCPV
Spontaneous CP violation Spontaneous CP violation (SCPV) occurs when CP is a gooood symmetry of the
original Lagrangian but after SSB no CP symmetry remains (1973 TD Lee)
Renormalizable gauge theories are based on the SSB mechanism and it is
natural to have the SCPV as an integral part of that mechanism
In the SM it is not possible to have spontaneous CP violation and to violate CP
explicitly in the Higgs sector
The origin of the observed CKM CP violation
Explicitly violated by Yukawa couplings
SCPV in the Higgs potential (rarr More than 2)
We are in need of a fundamental understanding of the origin of CP violation
CP violation is one of the crucial ingredients necessary to generate
the observed Matter-antimatter asymmetry of the Universe as well as
to explain low energy CP violation
It is not enough for the SM CP violation to lead to the observed BAU
Non-zero 13 in neutrino oscillation Exps CP violations in the lepton sector
can strengthen our belief in the BAU originated from leptogenesis scenario
QCD θ problem Peccei-Quinn CP is violated softly or spontaneously
2013-05-30
Present Knowledges on Quark and Lepton sectors
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Cosmological limit (including WMAP 3-years result)
upper bound on neutrino masses
(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)
Starting to disfavor the degenerate spectrum of neutrinos
BAU Astrophys J Suppl 192 (2011) 18
the most plausiblehellipBUT difficult to direct test
at seesaw scale18 parameters at low energy 9 observables
2013-05-30
B 10of baryons(N )62
of photons1
)0
(NB
Where Do we Stand There are empirical fermion mass hierarchies in the charged leptons up- and down-type
quark sectors calculated from the measured values (PDG)
mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21
Quark mixing angles
2013-05-30
Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data
one can assume a flavor symmetry which may reduce the unknown parameters
Unless flavor symmetries are assumed particle masses and mixings are generally
undetermined in gauge theory
A4 Trsquo S4 S3helliphellip Discrete amp Non-Abelian
global
spontaneously broken at high-energy
broken by a set of scalar fields which transform only under the flavor sym
Symmetry
Breaking
2013-05-30
A4 Symmetry (Smallest group for three-families) A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects 42=12 elements Generator S and T with the relations S2=T3=(ST)3=I S2=I Z2 symmetry T3=I Z3 symmetry Elements I S T ST TS T2 ST2 STS TST T2S TST2 T2ST There are 4 irreducible representation 1 1 1 3
Ma amp Rajasekaran
Why A4
A4 is the smallest discrete group that has 3-dimensional irreducible representation
A4 flavor symmetry can give a micro- symmetric pattern
for experimental data
A4 flavor symmetry can provide SCPV
2013-05-30
1
3
4
2
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Spontaneous CP violation Spontaneous CP violation (SCPV) occurs when CP is a gooood symmetry of the
original Lagrangian but after SSB no CP symmetry remains (1973 TD Lee)
Renormalizable gauge theories are based on the SSB mechanism and it is
natural to have the SCPV as an integral part of that mechanism
In the SM it is not possible to have spontaneous CP violation and to violate CP
explicitly in the Higgs sector
The origin of the observed CKM CP violation
Explicitly violated by Yukawa couplings
SCPV in the Higgs potential (rarr More than 2)
We are in need of a fundamental understanding of the origin of CP violation
CP violation is one of the crucial ingredients necessary to generate
the observed Matter-antimatter asymmetry of the Universe as well as
to explain low energy CP violation
It is not enough for the SM CP violation to lead to the observed BAU
Non-zero 13 in neutrino oscillation Exps CP violations in the lepton sector
can strengthen our belief in the BAU originated from leptogenesis scenario
QCD θ problem Peccei-Quinn CP is violated softly or spontaneously
2013-05-30
Present Knowledges on Quark and Lepton sectors
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Cosmological limit (including WMAP 3-years result)
upper bound on neutrino masses
(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)
Starting to disfavor the degenerate spectrum of neutrinos
BAU Astrophys J Suppl 192 (2011) 18
the most plausiblehellipBUT difficult to direct test
at seesaw scale18 parameters at low energy 9 observables
2013-05-30
B 10of baryons(N )62
of photons1
)0
(NB
Where Do we Stand There are empirical fermion mass hierarchies in the charged leptons up- and down-type
quark sectors calculated from the measured values (PDG)
mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21
Quark mixing angles
2013-05-30
Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data
one can assume a flavor symmetry which may reduce the unknown parameters
Unless flavor symmetries are assumed particle masses and mixings are generally
undetermined in gauge theory
A4 Trsquo S4 S3helliphellip Discrete amp Non-Abelian
global
spontaneously broken at high-energy
broken by a set of scalar fields which transform only under the flavor sym
Symmetry
Breaking
2013-05-30
A4 Symmetry (Smallest group for three-families) A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects 42=12 elements Generator S and T with the relations S2=T3=(ST)3=I S2=I Z2 symmetry T3=I Z3 symmetry Elements I S T ST TS T2 ST2 STS TST T2S TST2 T2ST There are 4 irreducible representation 1 1 1 3
Ma amp Rajasekaran
Why A4
A4 is the smallest discrete group that has 3-dimensional irreducible representation
A4 flavor symmetry can give a micro- symmetric pattern
for experimental data
A4 flavor symmetry can provide SCPV
2013-05-30
1
3
4
2
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Present Knowledges on Quark and Lepton sectors
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Cosmological limit (including WMAP 3-years result)
upper bound on neutrino masses
(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)
Starting to disfavor the degenerate spectrum of neutrinos
BAU Astrophys J Suppl 192 (2011) 18
the most plausiblehellipBUT difficult to direct test
at seesaw scale18 parameters at low energy 9 observables
2013-05-30
B 10of baryons(N )62
of photons1
)0
(NB
Where Do we Stand There are empirical fermion mass hierarchies in the charged leptons up- and down-type
quark sectors calculated from the measured values (PDG)
mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21
Quark mixing angles
2013-05-30
Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data
one can assume a flavor symmetry which may reduce the unknown parameters
Unless flavor symmetries are assumed particle masses and mixings are generally
undetermined in gauge theory
A4 Trsquo S4 S3helliphellip Discrete amp Non-Abelian
global
spontaneously broken at high-energy
broken by a set of scalar fields which transform only under the flavor sym
Symmetry
Breaking
2013-05-30
A4 Symmetry (Smallest group for three-families) A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects 42=12 elements Generator S and T with the relations S2=T3=(ST)3=I S2=I Z2 symmetry T3=I Z3 symmetry Elements I S T ST TS T2 ST2 STS TST T2S TST2 T2ST There are 4 irreducible representation 1 1 1 3
Ma amp Rajasekaran
Why A4
A4 is the smallest discrete group that has 3-dimensional irreducible representation
A4 flavor symmetry can give a micro- symmetric pattern
for experimental data
A4 flavor symmetry can provide SCPV
2013-05-30
1
3
4
2
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Cosmological limit (including WMAP 3-years result)
upper bound on neutrino masses
(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)
Starting to disfavor the degenerate spectrum of neutrinos
BAU Astrophys J Suppl 192 (2011) 18
the most plausiblehellipBUT difficult to direct test
at seesaw scale18 parameters at low energy 9 observables
2013-05-30
B 10of baryons(N )62
of photons1
)0
(NB
Where Do we Stand There are empirical fermion mass hierarchies in the charged leptons up- and down-type
quark sectors calculated from the measured values (PDG)
mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21
Quark mixing angles
2013-05-30
Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data
one can assume a flavor symmetry which may reduce the unknown parameters
Unless flavor symmetries are assumed particle masses and mixings are generally
undetermined in gauge theory
A4 Trsquo S4 S3helliphellip Discrete amp Non-Abelian
global
spontaneously broken at high-energy
broken by a set of scalar fields which transform only under the flavor sym
Symmetry
Breaking
2013-05-30
A4 Symmetry (Smallest group for three-families) A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects 42=12 elements Generator S and T with the relations S2=T3=(ST)3=I S2=I Z2 symmetry T3=I Z3 symmetry Elements I S T ST TS T2 ST2 STS TST T2S TST2 T2ST There are 4 irreducible representation 1 1 1 3
Ma amp Rajasekaran
Why A4
A4 is the smallest discrete group that has 3-dimensional irreducible representation
A4 flavor symmetry can give a micro- symmetric pattern
for experimental data
A4 flavor symmetry can provide SCPV
2013-05-30
1
3
4
2
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Cosmological limit (including WMAP 3-years result)
upper bound on neutrino masses
(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)
Starting to disfavor the degenerate spectrum of neutrinos
BAU Astrophys J Suppl 192 (2011) 18
the most plausiblehellipBUT difficult to direct test
at seesaw scale18 parameters at low energy 9 observables
2013-05-30
B 10of baryons(N )62
of photons1
)0
(NB
Where Do we Stand There are empirical fermion mass hierarchies in the charged leptons up- and down-type
quark sectors calculated from the measured values (PDG)
mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21
Quark mixing angles
2013-05-30
Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data
one can assume a flavor symmetry which may reduce the unknown parameters
Unless flavor symmetries are assumed particle masses and mixings are generally
undetermined in gauge theory
A4 Trsquo S4 S3helliphellip Discrete amp Non-Abelian
global
spontaneously broken at high-energy
broken by a set of scalar fields which transform only under the flavor sym
Symmetry
Breaking
2013-05-30
A4 Symmetry (Smallest group for three-families) A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects 42=12 elements Generator S and T with the relations S2=T3=(ST)3=I S2=I Z2 symmetry T3=I Z3 symmetry Elements I S T ST TS T2 ST2 STS TST T2S TST2 T2ST There are 4 irreducible representation 1 1 1 3
Ma amp Rajasekaran
Why A4
A4 is the smallest discrete group that has 3-dimensional irreducible representation
A4 flavor symmetry can give a micro- symmetric pattern
for experimental data
A4 flavor symmetry can provide SCPV
2013-05-30
1
3
4
2
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Where Do we Stand Latest 3 neutrino global analysis including atm solar reactor (Double Chooz)
LBL (T2KMINOS)
And the latest Daya Bay and RENO results
(arXiv 1209 3023 Gonzalez-Garcia Maltoni Salvado and Schwetz)
2013-02-26
Where Do we Stand Cosmological limit (including WMAP 3-years result)
upper bound on neutrino masses
(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)
Starting to disfavor the degenerate spectrum of neutrinos
BAU Astrophys J Suppl 192 (2011) 18
the most plausiblehellipBUT difficult to direct test
at seesaw scale18 parameters at low energy 9 observables
2013-05-30
B 10of baryons(N )62
of photons1
)0
(NB
Where Do we Stand There are empirical fermion mass hierarchies in the charged leptons up- and down-type
quark sectors calculated from the measured values (PDG)
mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21
Quark mixing angles
2013-05-30
Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data
one can assume a flavor symmetry which may reduce the unknown parameters
Unless flavor symmetries are assumed particle masses and mixings are generally
undetermined in gauge theory
A4 Trsquo S4 S3helliphellip Discrete amp Non-Abelian
global
spontaneously broken at high-energy
broken by a set of scalar fields which transform only under the flavor sym
Symmetry
Breaking
2013-05-30
A4 Symmetry (Smallest group for three-families) A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects 42=12 elements Generator S and T with the relations S2=T3=(ST)3=I S2=I Z2 symmetry T3=I Z3 symmetry Elements I S T ST TS T2 ST2 STS TST T2S TST2 T2ST There are 4 irreducible representation 1 1 1 3
Ma amp Rajasekaran
Why A4
A4 is the smallest discrete group that has 3-dimensional irreducible representation
A4 flavor symmetry can give a micro- symmetric pattern
for experimental data
A4 flavor symmetry can provide SCPV
2013-05-30
1
3
4
2
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Where Do we Stand Cosmological limit (including WMAP 3-years result)
upper bound on neutrino masses
(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)
Starting to disfavor the degenerate spectrum of neutrinos
BAU Astrophys J Suppl 192 (2011) 18
the most plausiblehellipBUT difficult to direct test
at seesaw scale18 parameters at low energy 9 observables
2013-05-30
B 10of baryons(N )62
of photons1
)0
(NB
Where Do we Stand There are empirical fermion mass hierarchies in the charged leptons up- and down-type
quark sectors calculated from the measured values (PDG)
mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21
Quark mixing angles
2013-05-30
Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data
one can assume a flavor symmetry which may reduce the unknown parameters
Unless flavor symmetries are assumed particle masses and mixings are generally
undetermined in gauge theory
A4 Trsquo S4 S3helliphellip Discrete amp Non-Abelian
global
spontaneously broken at high-energy
broken by a set of scalar fields which transform only under the flavor sym
Symmetry
Breaking
2013-05-30
A4 Symmetry (Smallest group for three-families) A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects 42=12 elements Generator S and T with the relations S2=T3=(ST)3=I S2=I Z2 symmetry T3=I Z3 symmetry Elements I S T ST TS T2 ST2 STS TST T2S TST2 T2ST There are 4 irreducible representation 1 1 1 3
Ma amp Rajasekaran
Why A4
A4 is the smallest discrete group that has 3-dimensional irreducible representation
A4 flavor symmetry can give a micro- symmetric pattern
for experimental data
A4 flavor symmetry can provide SCPV
2013-05-30
1
3
4
2
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Where Do we Stand There are empirical fermion mass hierarchies in the charged leptons up- and down-type
quark sectors calculated from the measured values (PDG)
mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21
Quark mixing angles
2013-05-30
Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data
one can assume a flavor symmetry which may reduce the unknown parameters
Unless flavor symmetries are assumed particle masses and mixings are generally
undetermined in gauge theory
A4 Trsquo S4 S3helliphellip Discrete amp Non-Abelian
global
spontaneously broken at high-energy
broken by a set of scalar fields which transform only under the flavor sym
Symmetry
Breaking
2013-05-30
A4 Symmetry (Smallest group for three-families) A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects 42=12 elements Generator S and T with the relations S2=T3=(ST)3=I S2=I Z2 symmetry T3=I Z3 symmetry Elements I S T ST TS T2 ST2 STS TST T2S TST2 T2ST There are 4 irreducible representation 1 1 1 3
Ma amp Rajasekaran
Why A4
A4 is the smallest discrete group that has 3-dimensional irreducible representation
A4 flavor symmetry can give a micro- symmetric pattern
for experimental data
A4 flavor symmetry can provide SCPV
2013-05-30
1
3
4
2
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data
one can assume a flavor symmetry which may reduce the unknown parameters
Unless flavor symmetries are assumed particle masses and mixings are generally
undetermined in gauge theory
A4 Trsquo S4 S3helliphellip Discrete amp Non-Abelian
global
spontaneously broken at high-energy
broken by a set of scalar fields which transform only under the flavor sym
Symmetry
Breaking
2013-05-30
A4 Symmetry (Smallest group for three-families) A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects 42=12 elements Generator S and T with the relations S2=T3=(ST)3=I S2=I Z2 symmetry T3=I Z3 symmetry Elements I S T ST TS T2 ST2 STS TST T2S TST2 T2ST There are 4 irreducible representation 1 1 1 3
Ma amp Rajasekaran
Why A4
A4 is the smallest discrete group that has 3-dimensional irreducible representation
A4 flavor symmetry can give a micro- symmetric pattern
for experimental data
A4 flavor symmetry can provide SCPV
2013-05-30
1
3
4
2
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
A4 Symmetry (Smallest group for three-families) A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects 42=12 elements Generator S and T with the relations S2=T3=(ST)3=I S2=I Z2 symmetry T3=I Z3 symmetry Elements I S T ST TS T2 ST2 STS TST T2S TST2 T2ST There are 4 irreducible representation 1 1 1 3
Ma amp Rajasekaran
Why A4
A4 is the smallest discrete group that has 3-dimensional irreducible representation
A4 flavor symmetry can give a micro- symmetric pattern
for experimental data
A4 flavor symmetry can provide SCPV
2013-05-30
1
3
4
2
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
The Model
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Construction of Lagrangian Under SU(2)timesU(1) we impose
A4 flavor symmetry for leptons quarks and scalars
CP invariance at the Lagrangian level which implies that all the parameters
appearing in the Lagrangian are real
the extended Higgs sector can spontaneously break CP through a phase
in the VEV of the gauge-singlet scalar field
in the three dimensional real representation the CP-invariance can be
guaranteed by (Holthusen Lindner and Schmidt JHEP 1304 122)
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Construction of Lagrangian
auxiliary Z2 symmetry
This non-flavor symmetry forbids some irrelevant Yukawa terms from the quark Lagrangian
an unique CP source in quark Yukawa Lagrangian
Instead of this one can use a continuous global U(1)PQ symmetry but low energy axions are already excluded
High energy axionshellipheavy gauge singlet scalarhellip
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
Self-interaction terms are manifestly well-behaved
The relative phases j themselves are dynamically determined
The relative phases of and do not provide a CP-violating source
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Higgs potential Lagrangian The most general renormalizable scalar potential under SU(2)timesU(1)timesA4timesZ2timesCP
In the presence of two A4 triplet Higgs scalars problematic interaction terms in V()
unnatural fine-tuning conditions have to be executed
in the limit where the seesaw scale field decouples from the EW scale fields
and
we wish these couplings to be sufficiently small (could not deform a demanded VEV alignment)
Even the potential V() does not deform a desirable VEV alignment without loss of generality we switch off the couplings in V()
Such stability problem can be naturally solved for instance in the presence of discrete sym (PRD 86093003) or extra-dimension (NPB 741 215) or in supersymmetric dynamical completions (JHEP 0604039)
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Spontaneous CP violation Once the singlet acquires a complex VEV the CP symmetry is spontaneously broken at
high energies by the complex VEV of the scalar singlet Such a breaking leads to CKM and
PMNS CP violation at low energies as well as a natural source of Leptogenesis
Minimization of the neutral scalar potential
After the breaking of flavor and electroweak symmetry
The phases j j are dynamically determined by minimizing the Higgs
potential
We obtain seesaw VEV
2013-05-30
A non-trivial seesaw VEV configuration
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Spontaneous CP violation For this vacuum alignment
there are other three possible solutions to the above
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Spontaneous CP violation The electroweak VEV configuration for and fields
We have let j=0 without loss of generality due to [(dagger) (dagger)]1
For this vacuum alignment
there are two solutions for =0 plusmn and =plusmn2 but they do not violate CP
2013-05-30
A non-trivial electroweak VEV configuration
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Quark Sector Quark Yukawa interactions invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Quark Sector Quark Yukawa interactions (d5) including dimension-5 operators driven by -field
invariant under SU(2)timesU(1)timesA4timesZ2timesCP
Each flavor of up-(down-)type quarks has three independent Yukawa terms
the terms involve the A4 triplets and QL
The right-handed (up down)-type quarks are eigenstates of T with eigenvalues
1 2 respectively =exp(2i3)
(uRdR)1 (cRsR)2 (tRbR)
A4 triplet scalar field drives the dimension-5 operators
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Quark Sector VEVs alignment of A4 triplets
Up-type quark
Down-type quark
where
2013-05-30
VCKM=[U]dagger[U]=I + Corrections
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Quark Sector For the most natural case of hierarchical quark Yukawa couplings
yf3yf2yf1 (fi i-th generation of f-type quark)
The off-diagonal elements generated by the higher dimensional operators are
generally smaller in magnitude than the diagonal ones
Only the mixing matrix takes part in CKM matrix
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Quark Sector Empirical fermion mass ratios in the up- and down-type quark sector (PDG 2011)
the mass spectrum of the up-type quarks exhibits a much stronger
hierarchical pattern to that of the down-type quarks
In terms of the Cabbibo angle sinC|Vus|
(mdms)(4 2)mb and (mumc)(8 4)mt
Due to the measured value of mumt it is impossible to generate the Cabbibo angle
If let
in discrepancy with the measured
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Quark Sector
From the measured down-type quark mass hierarchies
for letting
which in turn means should be 06 3
In order to get the correct CKM that is
we need plausible assumption
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
CKM mixing matrix In the weak eigenstate basis the quark mass terms and the charged gauge interactions
Using
With the fields redefinitions and letting
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
A strong CP solution The term associated with the strong CP problem
Experimental bounds on CP violation EDM of neutron dnlt02910-25 e
|eff|lt05610-10
it should be very small to make a theory consistent with experimental bounds
A huge cancellation between and arg[det(ud)] suggests that there should
be a physical process
At tree level the strong CP problem is automatically solved
Including higher dimensional operators the situation is changed
However with the requirement
One can suppress the contributions of higher dimensional operators
(hellip) combinations of
The up-type quark masses are much stronger than the down type one
the CKM is (or mainly) generated by the down-type quark sector
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Lepton Sector Yukawa interactions (d5) in the neutrino and charged lepton sectors invariant under
SU(2)timesU(1)timesA4timesZ2timesCP
Minimal Yukawa couplings
Each Dirac-like and charged-lepton sector has three independent Yukawa terms
A non-degenerate Dirac-neutrino Yukawa matrix
Heavy s acquire a bare mass term M and a mass induced by field
Non-trivial breaking pattern ltχgt=ei(100) gives an unique CP phase
The three leptons e micro are eigenstates of T with eigenvalues 1 2
respectively =exp(2i3) Le1 Lmicro2 L
eR1 microR2 R
As a consequence the charged lepton mass matrix automatically diagonal
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Lepton Sector In a weak eigenstate basis
the leptonic mass terms and the charged gauge interactions
VEV alignments of A4 triplet and singlet
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Leptonic CP source Performing basis rotation
Right-handed Mj Neutrino mass matrix
Dirac-neutrino Yukawa matrix
2013-05-30
Non-zero θ13 amp Leptonic CP violation
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Low energy Phenomenology After seesawing
In the limit y2rarry3 the above matrix goes to micro- symmetry leading to θ13=0 and θ23=45 In the limit y2=y3 rarr1 TBM θ13=0 θ23=45 and θ12=sin-1(1radic3)
Leptonic CP violation
2013-05-30
Non-zero 13 requires deviations of y2 y3 from unit
in turn implying a possibility of Leptonic CP violation
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Mixing Angles We take 1012 GeV as a cut-off scale and M=1011GeV as a seesaw scale
In neutrino mass matrix the five inputs (m0 y2 y3 ) can be determined
by the Exp data ( 12 13 23 )
( here )
CP phases can be predicted after determining model parameters
Reactor angle θ13 Vs the CP source
NMH +
IMH
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Mixing Angles
Leptonic CP violation Vs Reactor angle θ13 Dirac-phase δCP Vs Reactor angle θ13
NMH +
IMH
Our model makes prediction for the Dirac-CP phase in NMH and IMH which can be
tested in near future neutrino oscillation Exps
For the values of giving the CKM CP-phase IMH NMH
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Mixing Angles
Atm angle θ23 Vs Reactor angle θ13 Solar angle θ12 Vs Reactor angle θ13
For the values of giving the right CKM CP phase NMH favors 23gt45 and 23lt45 (but small deviations from the maximality) while IMH favors 23lt45 with large
deviations from maximality
No correlation between solar mixing angle and reactor angle
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Leptogenesis We are in the energy scale where A4 symmetry is broken but the SM gauge group
remains unbroken
NirarrL +CP-conjugate
A non-trival CP-violating phase in the one loop diagrams
CP-Asymmetry relevant for leptogenesis is associated with the neutrino Yukawa coupling matrix itself and its combination
Non-zero entries and imaginaries deviation y2 y3 from unit 12 ()
Mild deviations y2 y3 from unit
a successful leptogenesis scale1010-1012 GeV due to equal size of moduli of
neutrino Yukawa couplings (strong-washout)
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Due to the leptogenesis scale M=1011GeV two-flavored leptogenesis is considered
B Vs θ13 CP Vs lB
NMH
IMH +
Leptogenesis scale = 1011GeV neutrino Yukawa coupling
less than 109 GeV -gt difficult to obtain a successful leptogenesis
above 1012 GeV -gt hard to fit the right value of B onto the measured 13
With a successful leptogenesis the PMNS Dirac CP-phase is more constrained
2013-02-26
Leptogenesis
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
Conclusions
the spontaneously generated CP phase ldquordquocould become a natural source of
leptogenesis as well as CP violations in the CKM and PMNS
We have provided a solution for the strong CP problem
For =90-140 the quarks lead to the correct CKM CP-phase while leptons predict
the Dirac CP-phase in PMNS
Considering a successful leptogenesis predictions of the PMNS Dirac CP phase could be more constrained
2013-05-30
