1. Leptonic CP Violation & Wolfenstein Parametrization For Lepton Mixing in Gauge Family Model Yue-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

2. Brief Introduction to Neutrinos 1930 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 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: ½ 1969 Gribov & Pontecorvo Majorana-type Neutrino Mixing

3. 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

4. 2012 more precise measurement 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

5. General Formalism ： Neutrino Oscillation L-baseline, E-neutrino energy, V- effective matter potential

6. 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

7. Global Fitting Based on Experimental Data M.C. Gonzalez-Garcia, M. Maltoni, J. Salvado and T. Schwetz, JHEP 1212, 123 (2012); arXiv: 1209.3023.

8. Global Fitting Based on Experimental Data D. V. Forero, M. Tortola, and J. W. F. Valle, Phys. Rev. D86, 073012 (2012); arXiv:1205.4018.

9. 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

10. 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 ?

11. Other Theoretical Questions  Why neutrino masses are so small  Mass hierarchy  m 31 2 > 0 ？  m 31 2 < 0 ？  Why neutrino mixings are so large in comparison with quark mixings  Possible relation between CKM & MNSP  Family Symmetry?

12. 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): 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]

13.  N Fukugita & Yanagida (1986): Leptogenesis Mechanism Seesaw Mechanism

14. Tri-Bimaximal Mixing: (Harrison,Perkins and Scott) Family Symmetry Exact Discrete symmetry  Tri-bimaximal mixing with  13 = 0 Based SO(3) gauge family symmetry : ( YLWu, 2008 PRD)

18. SU(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

19. In terms of SU(3) representation with Z_2 symmetry (2--3): Fixing gauge : Z_2 symmetry invariant Lagrangian Why Local SU(3) Family Symmetry

20. In terms of SU(3) Representation SU(3) Expression of Tri-triplet Higgs Bosons Vacuum Structure

21. Standard Sea-saw Mechanism Standard Sea-saw Mechanism Neutrino Mass: Charged-lepton Mass :

22. 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

23. 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 !!!

24. Approximate Global U(1) Family Symmetries ~ U(1)_1 x U(1)_2 x U(1)_3 Exact Tri-bimaximal Neutrino Mixing ~

25. Leptonic CP Violation & Wofenstein Parametrization 轻子混合矩阵与 CP 破坏、 Wolfenstein 参数化

26. Leptonic CP Violation & Wofenstein Parametrization 轻子混合矩阵与 CP 破坏、 Wolfenstein 参数化

28. 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

33. From Global Fitting by Fogli et.al. Leptonic Wolfenstein Parameters and Majorana Phases

34. With Cabbibo Angle & Central Values Leptonic Wolfenstein Parameters, CP Phase, Majorana Phases v.s. Quark Wolfenstein Parameters, CP Phase

36. Neutrino Masses 中微子质量 Neutrino Masses Heavy Majorana Masses

37. 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

38. 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

39.  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

40. THANKS THANKS