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