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Yue-Liang Wu Kavli Institute for Theoretical Physics China (KITPC)

海峡两岸 “ 粒子物理和宇宙学”研讨会 CSW-PPC2014. 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

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Yue-Liang Wu Kavli Institute for Theoretical Physics China (KITPC)

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  1. 海峡两岸“粒子物理和宇宙学”研讨会CSW-PPC2014海峡两岸“粒子物理和宇宙学”研讨会CSW-PPC2014 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)

  2. Brief Introduction to Neutrinos 1930 Pauli (30 years old)： Neutrino withs=1/2、NWIP、m < m_e To solve energy conservation problem and spin- statistical probleminvolved 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) 1998.6Super-Kamiokande Experiment Evidence of Massive Neutrinos & Neutrino Oscillations 1998-2011 more experiments for mixing angles & mass-square differences • Solar Neutrino: SNO，Super-K • Atmosphere Neutrino: Super-K • Reactor Neutrino: KamLAND， CHOOZ • Accelerator: K2K，MINOS，T2K

  4. 2012 more precise measurement Double Chooz Experimental Y. Abe et al. [Double Chooz Collaboration], PRL 108, 131801 (2012) , arXiv:1112.6353 Daya Bay Experiment: F. P. An et al. [DAYA-BAY Collaboration], PRL 108, 171803 (2012), arXiv:1203.1669 RENO Experimental PRL 108, 191802 (2012) , arXiv:1204.0626

  5. Neutrino Oscillation General Formalism： 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) YLWu, Physics Letters B 714 (2012) 286–294, arXiv: 1203.2382 Maximal CP violation: 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 m312 > 0 ？m312 < 0？  Why neutrino mixings are so large in comparison with quark mixings Possible relation between CKM & MNSP  Family Symmetry?

  12. Issues in Neutrino Physics 1. Dirac / Majorana Neutrinoless Double Beta Decay 2. Mass scale: m Neutrinoless Double Beta Decay, Single Beta Decay, Cosmology 1. Cosmology (CMB+LSS): Planck: 0.025-0.1 eV 2. Single Beta Decay KATRIN: 0.2 eV CUORE: 0.02-0.1 eV 3. Neutrinoless Double Beta Decay HD Cuoricini NEMO3 Bilenky, Giunti, arXiv:1203.5250v3[hep-ph]

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

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

  15. SU(3) Gauge Family Model 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 • 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

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

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

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

  19. 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

  20. 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 !!!

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

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

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

  24. 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

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

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

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

  28. 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 Two inputs: with given parameter and

  29. 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

  30. Summary & Remarks • 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.

  31. THANKS

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