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Leptonic CP Violation & Wolfenstein Parametrization For
Lepton Mixing in Gauge Family ModelYue-Liang Wu
Kavli Institute for Theoretical Physics China (KITPC)
State Key Laboratory of Theoretical Physics (SKLTP)
ITP-CAS
University of Chinese Academy of Sciences (UCAS)
海峡两岸“粒子物理和宇宙学”研讨会 CSW-PPC2014
Brief Introduction to Neutrinos1930 Pauli (30 years old): Neutrino with s=1/2 、 NWIP 、 m < m_eTo solve energy conservation problem and spin- statistical
problem involved in decay
1962 Lederman, Schwartz & Steinberge
Observed _ at Brookhaven (NP)
1962 MNS – Maki-Nakagawa-Sakata
Lepton Mixing Angle: 1967 R. Davis Solar Neutrino Exp. Neutrino missing puzzle
1967 Pontecorvo _e _
Solar Neutrino Puzzle: ½1969 Gribov & Pontecorvo Majorana-type Neutrino Mixing
1977-79 See-Saw Mechanism & GUTs 1978 Matter Effects , L. Wolfenstein
1986 S.P. Mikheyev and A. Yu. Smirnov Matter Effects of Neutrino Oscillations (MSW)
Solar Neutrino: SNO , Super-K Atmosphere Neutrino: Super-K Reactor Neutrino: KamLAND , CHOOZ Accelerator: K2K , MINOS , T2K
1998.6 Super-Kamiokande Experiment Evidence of Massive Neutrinos & Neutrino Oscillations
1998-2011 more experiments for mixing angles & mass-square differences
2012 more precise measurement
13
F. P. An et al. [DAYA-BAY Collaboration], PRL 108, 171803 (2012), arXiv:1203.1669
Daya Bay Experiment:
RENO Experimental PRL 108, 191802 (2012) , arXiv:1204.0626
Y. Abe et al. [Double Chooz Collaboration], PRL 108, 131801 (2012) , arXiv:1112.6353
Double Chooz Experimental
iα ii
U
3
1
2
:
Mixing Angel
Mass Difference m
:Osci l l at i on parameters:
General Formalism:Neutrino Oscillation
L-baseline, E-neutrino energy, V- effective matter potential
Global Fitting Based on Experimental Data
G.L. Fogli, E. Lisi, A.Marrone, D.Montanino and A. Palazzo, Phys. Rev. D86, 013012 (2012); arXiv: 1205.5254
Global Fitting Based on Experimental Data
M.C. Gonzalez-Garcia, M. Maltoni, J. Salvado and T. Schwetz, JHEP 1212, 123 (2012); arXiv: 1209.3023.
Global Fitting Based on Experimental Data
D. V. Forero, M. Tortola, and J. W. F. Valle, Phys. Rev. D86, 073012 (2012); arXiv:1205.4018.
Theoretical Prediction Based on:
SU(3) gauge symmetry and Z_2 symmetry + ~ U(1)
Theoretical Prediction:
SU(3) gauge symmetry and Z_2 symmetry, ~ U(1)
Maximal CP violation:
YLWu, Physics Letters B 714 (2012) 286–294, arXiv: 1203.2382
Nearly Maximal 2-3 mixing
Unknown Questions:
Neutrinos are Dirac or Majorana?
Absolute Values of Neutrino Masses? Hierarchy or largely Degeneracy?
CP Violation in Lepton-Neutrino Sector?
How Many Neutrinos, Sterile Neutrinos?
Leptogenesis and Matter-Antimatter Asymmetry?
Rules of Neutrino in Astrophysics and Cosmology ?
Other Theoretical Questions
Why neutrino masses are so small
Mass hierarchy m312 > 0 ? m31
2 < 0 ? Why neutrino mixings are so large in
comparison with quark mixings
Possible relation between CKM & MNSP
Family Symmetry?
7 13~ 10 ~ 10e tm m m
1. Dirac / Majorana Neutrinoless Double Beta Decay
2. Mass scale: m Neutrinoless Double Beta Decay, Single Beta Decay, Cosmology
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
Planck: 0.025-0.1 eV
KATRIN: 0.2 eV
CUORE: 0.02-0.1 eV
HD
Cuoricini
NEMO3
Bilenky, Giunti, arXiv:1203.5250v3 [hep-ph]
N
h.c.n
MM
Mn
h.c.NMNNML
LR
TD
DcL
RRcRRDLY
0
2
1
2
1
R
cL
LN
n T
D1
RD MMMM v
Fukugita & Yanagida (1986):Leptogenesis Mechanism
Seesaw Mechanism
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 SOFamily Symmetry
Exact Discrete symmetry
Tri-bimaximal mixing with 13 = 0
Based SO(3) gauge family symmetry :
( YLWu, 2008 PRD)
SU(3) Gauge Family ModelSU(3) Gauge Family Model
Gauge Symmetry has been well tested
Why lepton sector is so different from quark sector ?
Neutrinos are neutral fermions and can be Majorana!
Invariant Lagrangian for Yukawa Interactions
YLWu, Physics Letters B 714 (2012) 286–294, arXiv: 1203.2382
Z. Liu, YLWu, PLB 30161, DOI: 10.1016/j.physletb.2014.04.049, arXiv:1403.2440
In terms of SU(3) representation with Z_2 symmetry (2--3):
Fixing gauge :
Z_2 symmetry invariant Lagrangian
Why Local SU(3) Family SymmetryWhy Local SU(3) Family Symmetry
In terms of SU(3) Representation
SU(3) Expression of Tri-triplet Higgs BosonsSU(3) Expression of Tri-triplet Higgs Bosons
Vacuum Structure
Standard Sea-saw MechanismStandard Sea-saw Mechanism
Neutrino Mass:
Charged-lepton Mass :
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 M_N >> v
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 !!!
Approximate Global U(1) Family SymmetriesApproximate Global U(1) Family Symmetries
~ U(1)_1 x U(1)_2 x U(1)_3
Exact Tri-bimaximal
Neutrino Mixing
~
Leptonic CP Violation & Wofenstein Parametrization
轻子混合矩阵与 CP破坏、Wolfenstein参数化
Leptonic CP Violation & Wofenstein Parametrization
轻子混合矩阵与 CP破坏、Wolfenstein参数化
Agree to the experimental data(PDG) within errors
Maximal CP Violation and CP-invariant Quantity 最大 CP破坏位相与 CP 破坏不变量
Leptonic CP Violation & Wofenstein Parametrization
轻子混合矩阵与 CP破坏、Wolfenstein参数化
From Global Fitting by Fogli et.al.
Leptonic Wolfenstein Parameters and Majorana Phases
With Cabbibo Angle & Central Values
Leptonic Wolfenstein Parameters, CP Phase, Majorana Phases
v.s. Quark Wolfenstein Parameters, CP Phase
Neutrino Masses 中微子质量 Neutrino Masses
Heavy Majorana Masses
Two inputs:
with given parameter and
Neutrino Masses 中微子质量
Normal spectrum 中微子质量的正常排序
Inverse Spectrum 中微子质量的反常排序
Total Mass 中微子总质量
Neutrino cosmology 中微子宇宙学
Summary and Remarks SU(3) gauge family symmetry is a natural
motivation from three families of quarks/leptons Smallness of neutrino masses and charged-
lepton mixing is understandable from approximate global U(1) family symmetries with standard see-saw mechanism.
Tri-bimaximal mixing in the neutrino sector is a consequence of Z_2 symmetry of the vacuum structure of SU(3) gauge family symmetry
The neutrino masses are largely degenerate and testable from next generation experiments & cosmology
The lepton mixing matrix can well be characterized by leptonic Wolfenstein parameters in the basis of tri-bimaximal neutrino mixing.
The leptonic CP violation has a strong correlation to the leptonic Wolfenstein parameters, a large or nearly maximal leptonic CP violation is favorable in a large region of parameters.
More precise measurements for the lepton mixing angles are very helpful
It is essential to have a direct measurement for the leptonic CP violationin near future.
Summary & Remarks
THANKSTHANKS