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KITPC Program on Neutrino Physics 2008.9.1-9.21
Nearly Tri-bimaximal Mixing
& Small Masses of Neutrinos
Yue-Liang WuKavli Institute for Theoretical Physics China
(KITPC)
Institute of Theoretical Physics
Chinese Academy of Sciences
78 Years Old Neutrino1930 Pauli (30 years old) : Neutrino with s=1/2 、 NWIP 、 m < m_e
To solve energy conservation problem and spin- statistical problem involved in decay
1933 Fermi: H_3 He_3 + e + anti- 1957 T.D.Lee & C.N.Yang: Parity Non-conservation (NP) C.S. Wu : Experimental Test1957 Landau, Lee & Yang, Salam Two Component Theory of Massless Neutrino m_ =0,
Maximal Parity Violation1958 Feynman-Gell-Mann, Marshak-Sudarshan V-A Theory1967 GWS Standard Model : SU(2)_L x U(1) (NP) Based on Massless Neutrinos
1957 Pontecorvo
Massive neutrinos 、 Neutrino Mixing & Oscillations
_e anti-_e
1957 R.Davis: Reactor Experiment
anti- + Cl_37 e + Ar_37
1962 Lederman, Schwartz & Steinberge
Observed _ at Brookhaven (NP)
1962 MNS – Maki-Nakagawa-Sakata
Lepton Mixing Angle: 1967 Pontecorvo
_e _
Solar Neutrino Puzzle: ½
1967 R. Davis Solar Neutrino Experiment (NP) 1969 Gribov & Pontecorvo Majorana-type Neutrino Mixing 1976 Bilenky & Pontecorvo Dirac-type Neutrino Mixing 1978 L. Wolfenstein; 1986 S.P. Mikheyev and A. Yu.
Smirnov Matter Effects of Neutrino Oscillations (MSW) 1979 See-Saw Mechanism & GUTs 1994 : ‘ 1 , 3 , 5 ’ - Massive , ‘ 2 , 4 , 6 ’ - Massless , 7 - No think 1998.6 Super-Kamiokande Experiment Evidence of Massive Neutrinos & Neutrino Oscillations
Answer Question: Massive or Massless?
Unknown Questions:
Neutrinos are Dirac or Majorana?
Absolute Values of Neutrino Masses? Hierarchy or Degeneracy?
CP Violation in Lepton-Neutrino Sector?
How Many Neutrinos, Sterile Neutrinos?
Leptogenesis and Matter-Antimatter Asymmetry?
Rules of Neutrino in Astrophysics and Cosmology ?
Theoretical Questions
Why neutrino masses are so small
Why neutrino mixings are so large in comparison with quark mixings
23 is exactly maximal ?
13 ? , Ue3 0 ?
Mass hierarchy m312 > 0 ? m31
2 < 0 ?
7 13~ 10 ~ 10e tm m m
1.01 6 2 1SSM 0.81
0.44 0.46 6 2 1SNO 0.43 0.43
Measured flux agrees with SSM
5.05 10 cm s
5.09 10 cm s
:
Flavor changing at 5.3
arXiv:nucl-ex/0610020
Electron neutrino generated from Sun
Solar Neutrino: SNOe
Oscillation parameters :2 0.10 0.10
sun 0.07 0.06
2 0.14 0.15 5 2sun 0.13 0.15
tan 0.56 (stat) (syst)
7.58 (stat) (syst) 10 eVm
arXiv:0801.4589
A scaled reactor spectrum without distortions from neutrino oscillationis excluded at more than 5σ!
Reactor neutrino: KamLAND
Cosmic-rayshower
0+
+
e
e+
Underground e,e,,
detector
Atmospheric neutrino source
+ + + e+ + e +
– – + e– + e +
~30 kilometers
θz
232atm
23
atm2
eV 104.3eV 105.1
12sin92.0
m
Atmosphere Neutrino: Super-K
Oscillation parameters :
iα ii
U
3
1
J. Valle et al. hep-ph/0405172, updated at Sep 2007
13 13 23 23
12 12 23 23
12 12 13 13
1 0 0 0 0 0 0
0 . 0 1 0 . 0 . 0 0
0 0 0 0 1 0 0 1
i i
iMNS
i
c s e c s e
U c s s c e
s c s e c
Solar : Super-K, SNOAtmosphere : Super-KReactor:KamLAND, CHOOZAccelerator:K2K , MINOS
2
:
Mixing Angel
Mass Difference m
:Osci l l at i on parameters:
General Formalism :Neutrino Oscillation
1. Dirac / Majorana Neutrinoless Double Beta Decay
2. Mass scale: m1
Neutrinoless Double Beta Decay, Single Beta Decay, Cosmology
3. Sterile neutrinos, LSND?
Excludes at 98% CL two-neutrino appearance oscillations as an explanation of the LSND anomaly. arXiv:0704.1500
MiniBooNE
(3+1): inconsistency at the level of 4σ. (3+2) ,(3+3): severe tension at the level of more than 3σ. arXiv:0705.0107
Issues in Neutrino Physics
2. Single Beta Decay
3. Neutrinoless Double Beta Decay
1. Cosmology (CMB+LSS):
0.61 eV (95% C.L.) WMAP 5 yearsim
i
ieiemUm )( 22
Troitsk eV2.2
Mainz eV3.2
e
e
m
m
|| 233
222
211 eeeee
UmUmUmm (0.35 1.24) eV (HM)
(0.33 1.35) eV (IGEX)ee
ee
m
m
Planck: 0.025-0.1 eV
KATRIN: 0.2 eV
CUORE: 0.02-0.1 eV
Strumia-Vissani arXiv:hep-ph/0503246
Neutrino Masses
3σ
arXiv:hep-ex/0509019
13
213
Daya Bay (90%CL)
Sin 2 0.01
Kam-Biu Luk, Jan 8 2007Int'l Symp on Neutrino Physics and Neutrino Cosmology
2 213 13Sin 0.050 Sin 2 0.19
Global fits:
N
h.c.nMM
Mn
h.c.NMNNML
LR
TD
DcL
RRcRRDLY
0
2
1
2
1
R
cL
LN
n
TD
1RD MMMM v
Fukugita & Yanagida (1986):Leptogenesis Mechanism
Type II? Type III?
Seesaw Mechanism
2(2) (1)L YSU U Z
0 ( ) / 2S iA
S or A may be Dark Matter!R. Barbieri, L. Hall and V.S. Rychkov, PRD 74, 015007, 2007
E. Ma, PRD 73, 077301, 2006
3 loop generation of neutrino masses: L.M. Krauss, S. Nasri and M. Trodden,
PRD 67, 085002, 2003
Right-handed neutrino as Dark Matter!
Other Mechanism for Neutrino MassesTwo Higgs doublets Model:
Tri-Bimaximal Mixing:
12 23 13
3 2Sin ;Sin ;Sin 0
3 2
6 30
3 3
6 3 2
6 3 2
6 3 2
6 3 2
MNSU
(Harrison,Perkins and Scott)
2 4, , (3)...Z A SO
Friedberg-Lee Symmetry:
Invariant under Friedberg-Lee symmetry: hep-ph/0606071
z a space-time independent constant element of the Grassmann algebra
Some papers:Xing, Zhang, Zhou, PLB641Luo, Xing, PLB 646C.S. Huang, T.J. Li, W. Liao and S.H. Zhu, arXiv:0803.4124
Family Symmetry
F. Harrison, D. H. Perkins and W. G. Scott, Phys. Lett. {\bf B 530}, 167 (2002) Z.-Z. Xing, Phys. Lett. {\bf B533}, 85(2002). P. F. Harrison and W.G. Scott, Phys. Lett. {\bf B535},163(2002). P.F. Harrison and W. G. Scott, Phys. Lett. {\bf B557},76(2003). X. G. He and A. Zee, Phys. Lett. {\bf B560}, 87(2003). C.I. Low and R. R. Volkas, Phys. Rev. {\bf D68}, 033007 (2003). E. Ma, Phys. Rev. {\bf D70}, 031901R(2004); E.Ma, hep-ph/0701016 G. Altarelli and F. Feruglio, Nucl. Phys. {\bf B720}, 64(2005); E. Ma, Phys. Rev. D72, 037301 (2005).; E. Ma, Mod.\ Phys.\ Lett.\ A 20, 2601 (2005) A. Zee, Phys. Lett. {\bf B630}, 58 (2005). E. Ma, Phys.\ Rev.\ D {\bf 73}, 057304 (2006). G. Altarelli and F. Feruglio, Nucl. Phys. {\bf B741}, 215(2006). W. Grimus and L. Lavoura, {\bf JHEP}, 0601:018(2006). J.E. Kim and J.-C. Park, {\bf JHEP} 0605:017(2006). N. Singh, M. Rajkhowa and A. Borach, hep-ph/0603189. R. Mohapatra, S. Naris and Y.-H. Yu, Phys.Lett. {\bf B639} 318 (2006). P. Kovtun and A. Zee, Phys.Lett. {\bf B640} (2006) 37. N. Haba, A. Watanabe and K. Yoshioka, Phys.Rev.Lett. 97 (2006) 041601. X.G. He, Y.Y. Keum and R. Volkas, {\bf JHEP}, 0604:039(2006). Varizelas, S.-F. King and G.G. Ross, Phys.Lett. B644 (2007) 153. R. Friedberg and T. D. Lee, arXiv:hep-ph/0606071; arXiv:hep-ph/0705.4156 B.Hu, F. Wu and Y.L. Wu, Phys.Rev. {\bf D75} 113003 (2007).
SO(3) Gauge Model
Exact Discrete symmetry
Tri-bimaximal with 13 = 0
Experimental Data (99%)
Gauge Symmetry has been well tested
Why SO(3) Gauge Model? YLW arXiv:0708.0867, PRD 2008
Why lepton sector is so different from quark sector ?
Neutrinos are neutral fermions and can be Majorana!
Majorana fermions only have real representations
They possess orthogonal symmetry Invariant Lagrangian for
Yukawa Interactions
Uniqueness of Lagrangian & New Particles
Symmetry
SO(3) Expression of Tri-triplet Higgs Bosons
In terms of SO(3) representation:
Symmetry as Subgroup of SO(3) Discrete symmetric group:
Cyclic permutation group: Coset space :
Cyclic permuted form:
with i+j-1 mod. 3
Why Local SO(3) Symmetry Fixing Gauge: invariant Lagrangian
In terms of SO(3) Representation
Vacuum StructureWith the given fixing gauge:
Type-II like (generalized) see-saw mechanism
For neutrinos: For charged leptons:
Global U(1) Family Symmetries
For Infinite Large Majorana neutrino masses
Majorana neutrinos decouple Generating global U(1) family symmetries
U(1)_1 x U(1)_2 x U(1)_3
Large but Finite Majorana Neutrino Masses ???
Small Mass and Large Mixing of Neutrinos
Approximate global U(1) family symmetries
Smallness of neutrino masses and charged lepton mixing
Neutrino mixings could be large !!!
Nearly Tri-bimaximal neutrino mixings Neutrino and charged lepton mixings:
≈
Lepton Mixing Matrix and Neutrino Masses
CKM-like Lepton mixing:
Neutrino Masses
Heavy Majorana Masses
Numerical Results 4 Parameters: / / Two inputs:
Neutrino masses with given parameter
Considering the hierarchy: One parameter in Vacuum:
Interesting case:
Two cases for charged lepton mixing:
13
Numerical results for given parameter
13
Taking
Optimistic Predictions
Which can be detected by the future neutrino Experiments, like Daya Bay
Vector-Like Heavy Neutrino and Charged Lepton Masses
Taking and
It leads to and
Taking
The lightest vector-like charged lepton mass
Which may be detected at LHC/ILC
Summary Smallness of neutrino masses and charged lepton
mixing could be understood from approximate global U(1) family symmetries
Tri-bimaxiaml neutrino mixing is obtainable from the vacuum structure of SO(3) gauge symmetry
13 is in general non-zero and testable at the
experimental sensitivity Some of the vector-like fermions could have
masses at electroweak scale and be probed at LHC The mechanism can simply be extended to quark
sector for smallness of quark mixing
THANKSTHANKS