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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
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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
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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
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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
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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
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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
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Global Fitting Based on Experimental Data
M.C. Gonzalez-Garcia, M. Maltoni, J. Salvado and T. Schwetz, JHEP 1212, 123 (2012); arXiv: 1209.3023.
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Global Fitting Based on Experimental Data
D. V. Forero, M. Tortola, and J. W. F. Valle, Phys. Rev. D86, 073012 (2012); arXiv:1205.4018.
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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
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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 ?
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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
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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]
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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
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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)
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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
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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
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In terms of SU(3) Representation
SU(3) Expression of Tri-triplet Higgs BosonsSU(3) Expression of Tri-triplet Higgs Bosons
Vacuum Structure
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Standard Sea-saw MechanismStandard Sea-saw Mechanism
Neutrino Mass:
Charged-lepton Mass :
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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
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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 !!!
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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
~
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Leptonic CP Violation & Wofenstein Parametrization
轻子混合矩阵与 CP破坏、Wolfenstein参数化
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Leptonic CP Violation & Wofenstein Parametrization
轻子混合矩阵与 CP破坏、Wolfenstein参数化
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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
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From Global Fitting by Fogli et.al.
Leptonic Wolfenstein Parameters and Majorana Phases
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With Cabbibo Angle & Central Values
Leptonic Wolfenstein Parameters, CP Phase, Majorana Phases
v.s. Quark Wolfenstein Parameters, CP Phase
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Neutrino Masses 中微子质量 Neutrino Masses
Heavy Majorana Masses
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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
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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
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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
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THANKSTHANKS