KITPC Program on Neutrino Physics 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 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 1933 Fermi: H_3  He_3 + e + anti 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

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

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 Super-Kamiokande Experiment Evidence of Massive Neutrinos & Neutrino Oscillations Answer Question: Massive or Massless?

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 ?

Theoretical Questions  Why neutrino masses are so small  Why neutrino mixings are so large in comparison with quark mixings   23 is exactly maximal ？   13 ? ， U e3  0 ？  Mass hierarchy  m 31 2 > 0 ？  m 31 2 < 0 ？

Flavor changing at 5.3  arXiv:nucl-ex/ Electron neutrino generated from Sun Solar Neutrino: SNO

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

Atmosphere Neutrino: Super-K Oscillation parameters ：

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

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

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

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

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

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

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

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}, (2003). E. Ma, Phys. Rev. {\bf D70}, R(2004); E.Ma, hep-ph/ G. Altarelli and F. Feruglio, Nucl. Phys. {\bf B720}, 64(2005); E. Ma, Phys. Rev. D72, (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}, (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/ 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) 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/ ; arXiv:hep-ph/ B.Hu, F. Wu and Y.L. Wu, Phys.Rev. {\bf D75} (2007).

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

Why SO(3) Gauge Model? YLW arXiv: , 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

Uniqueness of Lagrangian & New Particles  Symmetry 

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

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

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

Vacuum Structure With the given fixing gauge:

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

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  ???

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 !!!

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

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

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

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

Numerical results for given parameter

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

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

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

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