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Nearly Tri-bimaximal Mixing & Small Masses of Neutrinos

KITPC Program on Neutrino Physics 2008.9.1-9.21. Nearly Tri-bimaximal Mixing & Small Masses of Neutrinos. Yue-Liang Wu Kavli Institute for Theoretical Physics China (KITPC) Institute of Theoretical Physics Chinese Academy of Sciences. 78 Years Old Neutrino.

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Nearly Tri-bimaximal Mixing & Small Masses of Neutrinos

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  1. KITPC Program on Neutrino Physics 2008.9.1-9.21 Nearly Tri-bimaximal Mixing & Small Masses of Neutrinos Yue-Liang Wu Kavli Institute for Theoretical Physics China (KITPC) Institute of Theoretical Physics Chinese Academy of Sciences

  2. 78 Years Old Neutrino 1930 Pauli (30 years old)： Neutrino withs=1/2、NWIP、m < m_e To solve energy conservation problem and spin- statistical probleminvolved in  decay 1933 Fermi: H_3  He_3 + e + anti-  1957 T.D.Lee & C.N.Yang: Parity Non-conservation(NP) C.S. Wu： Experimental Test 1957 Landau, Lee & Yang, Salam Two Component Theory of Massless Neutrino m_ =0, Maximal Parity Violation 1958 Feynman-Gell-Mann, Marshak-Sudarshan V-A Theory 1967 GWS Standard Model： SU(2)_L x U(1) (NP) Based on Massless Neutrinos

  3. 1957 Pontecorvo Massive neutrinos、Neutrino Mixing & Oscillations _e  anti-_e 1957 R.Davis: Reactor Experiment anti-  + Cl_37  e + Ar_37 1962 Lederman, Schwartz & Steinberge Observed _ at Brookhaven (NP) 1962 MNS – Maki-Nakagawa-Sakata Lepton Mixing Angle: 1967 Pontecorvo _e _ Solar Neutrino Puzzle: ½

  4. 1967 R. Davis Solar Neutrino Experiment (NP) • 1969 Gribov & Pontecorvo Majorana-type Neutrino Mixing • 1976 Bilenky & Pontecorvo • Dirac-type Neutrino Mixing • 1978 L. Wolfenstein; 1986 S.P. Mikheyev and A. Yu. Smirnov Matter Effects of Neutrino Oscillations (MSW) • 1979 See-Saw Mechanism & GUTs • 1994： ‘1，3，5 ’ － Massive， ‘ 2，4，6 ’ －Massless， 7 － No think 1998.6Super-Kamiokande Experiment Evidence of Massive Neutrinos & Neutrino Oscillations Answer Question: Massive or Massless?

  5. Unknown Questions:  Neutrinos are Dirac or Majorana？  Absolute Values of Neutrino Masses？ Hierarchy or Degeneracy？  CP Violation in Lepton-Neutrino Sector？  How Many Neutrinos，Sterile Neutrinos？  Leptogenesis and Matter-Antimatter Asymmetry？  Rules of Neutrino in Astrophysics and Cosmology ?

  6. Theoretical Questions Why neutrino masses are so small Why neutrino mixings are so large in comparison with quark mixings 23is exactly maximal？  13?，Ue3 0？  Mass hierarchy m312 > 0 ？m312 < 0？

  7. Flavor changing at 5.3s Solar Neutrino: SNO Electron neutrino generated from Sun arXiv:nucl-ex/0610020

  8. Reactor neutrino: KamLAND arXiv:0801.4589 A scaled reactor spectrum without distortions from neutrino oscillation is excluded at more than 5σ! Oscillation parameters：

  9. Atmosphere Neutrino: Super-K Oscillation parameters：

  10. Neutrino Oscillation General Formalism： J. Valle et al. hep-ph/0405172, updated at Sep 2007 Solar： Super-K, SNO Atmosphere： Super-K Reactor:KamLAND, CHOOZ Accelerator:K2K，MINOS

  11. Issues in Neutrino Physics 1. Dirac / Majorana Neutrinoless Double Beta Decay 2. Mass scale: m1 Neutrinoless Double Beta Decay, Single Beta Decay, Cosmology 3. Sterile neutrinos, LSND? MiniBooNE Excludes at 98% CL two-neutrino appearance oscillations as an explanation of the LSND anomaly. arXiv:0704.1500 (3+1): inconsistency at the level of 4σ. (3+2) ,(3+3): severe tension at the level of more than 3σ. arXiv:0705.0107

  12. Neutrino Masses 1. Cosmology (CMB+LSS): Planck: 0.025-0.1 eV 2. Single Beta Decay KATRIN: 0.2 eV 3. Neutrinoless Double Beta Decay CUORE: 0.02-0.1 eV Strumia-Vissani arXiv:hep-ph/0503246

  13. Global fits: 3σ Kam-Biu Luk, Jan 8 2007 Int'l Symp on Neutrino Physics and Neutrino Cosmology arXiv:hep-ex/0509019

  14.  N Seesaw Mechanism Type II? Type III? Leptogenesis Mechanism Fukugita & Yanagida (1986):

  15. Other Mechanism for Neutrino Masses E. Ma, PRD 73, 077301, 2006 Two Higgs doublets Model: S or A may be Dark Matter! R. Barbieri, L. Hall and V.S. Rychkov, PRD 74, 015007, 2007 3 loop generation of neutrino masses: L.M. Krauss, S. Nasri and M. Trodden, PRD 67, 085002, 2003 Right-handed neutrino as Dark Matter!

  16. Family Symmetry Tri-Bimaximal Mixing: (Harrison,Perkins and Scott) Friedberg-Lee Symmetry: Some papers： Xing, Zhang, Zhou, PLB641 Luo, Xing, PLB 646 C.S. Huang, T.J. Li, W. Liao and S.H. Zhu, arXiv:0803.4124 hep-ph/0606071 Invariant under Friedberg-Lee symmetry: z a space-time independent constant element of the Grassmann algebra

  17. F. Harrison, D. H. Perkins and W. G. Scott, Phys. Lett. {\bf B 530}, 167 (2002) • Z.-Z. Xing, Phys. Lett. {\bf B533}, 85(2002). • P. F. Harrison and W.G. Scott, Phys. Lett. {\bf B535},163(2002). • P.F. Harrison and W. G. Scott, Phys. Lett. {\bf B557},76(2003). • X. G. He and A. Zee, Phys. Lett. {\bf B560}, 87(2003). • C.I. Low and R. R. Volkas, Phys. Rev. {\bf D68}, 033007 (2003). • E. Ma, Phys. Rev. {\bf D70}, 031901R(2004); E.Ma, hep-ph/0701016 • G. Altarelli and F. Feruglio, Nucl. Phys. {\bf B720}, 64(2005); • E. Ma, Phys. Rev. D72, 037301 (2005).; • E. Ma, Mod.\ Phys.\ Lett.\ A 20, 2601 (2005) • A. Zee, Phys. Lett. {\bf B630}, 58 (2005). • E. Ma, Phys.\ Rev.\ D {\bf 73}, 057304 (2006). • G. Altarelli and F. Feruglio, Nucl. Phys. {\bf B741}, 215(2006). • W. Grimus and L. Lavoura, {\bf JHEP}, 0601:018(2006). • J.E. Kim and J.-C. Park, {\bf JHEP} 0605:017(2006). • N. Singh, M. Rajkhowa and A. Borach, hep-ph/0603189. • R. Mohapatra, S. Naris and Y.-H. Yu, Phys.Lett. {\bf B639} 318 (2006). • P. Kovtun and A. Zee, Phys.Lett. {\bf B640} (2006) 37. • N. Haba, A. Watanabe and K. Yoshioka, Phys.Rev.Lett. 97 (2006) 041601. • X.G. He, Y.Y. Keum and R. Volkas, {\bf JHEP}, 0604:039(2006). • Varizelas, S.-F. King and G.G. Ross, Phys.Lett. B644 (2007) 153. • R. Friedberg and T. D. Lee, arXiv:hep-ph/0606071; arXiv:hep-ph/0705.4156 • B.Hu, F. Wu and Y.L. Wu, Phys.Rev. {\bf D75} 113003 (2007).

  18. SO(3) Gauge Model Exact Discrete symmetry  Tri-bimaximal with 13= 0 Experimental Data (99%) Gauge Symmetry has been well tested

  19. Why SO(3) Gauge Model?YLWarXiv:0708.0867, PRD 2008 • Why lepton sector is so different from quark sector ? Neutrinos are neutral fermions and can be Majorana! Majorana fermions only have real representations They possess orthogonal symmetry • Invariant Lagrangian for Yukawa Interactions

  20. Uniqueness of Lagrangian & New Particles • Symmetry

  21. SO(3) Expression of Tri-triplet Higgs Bosons In terms of SO(3) representation:

  22. Symmetry as Subgroup of SO(3) • Discrete symmetric group: • Cyclic permutation group: • Coset space : • Cyclic permuted form: with i+j-1 mod. 3

  23. Why Local SO(3) Symmetry • Fixing Gauge: • invariant Lagrangian • In terms of SO(3) Representation

  24. Vacuum Structure With the given fixing gauge:

  25. Type-II like (generalized) see-saw mechanism For neutrinos: For charged leptons:

  26. 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 • ???

  27. 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 !!!

  28. Nearly Tri-bimaximal neutrino mixings Neutrino and charged lepton mixings: ≈

  29. Lepton Mixing Matrix and Neutrino Masses CKM-like Lepton mixing: Neutrino Masses Heavy Majorana Masses

  30. Numerical Results 4 Parameters: / / Two inputs: Neutrino masses with given parameter

  31. Considering the hierarchy: One parameter in Vacuum: Interesting case: Two cases for charged lepton mixing:

  32. Numerical results for given parameter

  33. Taking Optimistic Predictions Which can be detected by the future neutrino Experiments, like Daya Bay

  34. Vector-Like Heavy Neutrino and Charged Lepton Masses Taking and It leads to and Taking The lightest vector-like charged lepton mass Which may be detected at LHC/ILC

  35. Summary • Smallness of neutrino masses and charged lepton mixing could be understood from approximate global U(1) family symmetries • Tri-bimaxiaml neutrino mixing is obtainable from the vacuum structure of SO(3) gauge symmetry • 13 is in general non-zero and testable at the experimental sensitivity • Some of the vector-like fermions could have masses at electroweak scale and be probed at LHC • The mechanism can simply be extended to quark sector for smallness of quark mixing

  36. THANKS

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