高能物理所 张贺 高能物理学会第七届年会 2006年10月29日 Based on the work by Z.Z. Xing, H. Zhang and S. Zhou, hep-ph/0607091, Phys. Lett. B 641(2006)189

Outline Introduction family symmetry Generalized Friedberg-Lee model from the family symmetry breaking Summary and discussion

? Introduction Lepton flavor mixing matrix: MNS matrix Current neutrino oscillation data at 99% CL range Mixing angles Mass differences ? Normal or Inverted A. Strumia and F. Vissani, hep-ph/0606054

Questions: Neutrino mixings are nearly tri-bimaximal P.F. Harrison, D.H. Perkins and W.G. Scott, PLB 530(2002)167 Trimaximal Bimaximal Questions: Why is almost maximal ? Why is so large ? Why is so small ? Does it vanish?

family symmetry Naturalness of theory: suppose a dimensionless small parameter a. If a->0, the symmetry is enhanced. In the limits interchange symmetry exists Remark: is arbitrary.

Discrete Family Symmetries S. Pakvasa and H. Sugawara, PLB 73(1978)61 S3 Z2 (mu-tau) A4 Tri-Bimaximal Mixing E. Ma and G. Rajasekaran, PRD 64 (2001) 113012 S4 S3×Z2, D4 … … E. Ma, PLB 632(2006)352

Friedberg-Lee model Neutrino mass operator hep-ph/0606071 Partial gauge-like symmetry: Consequential neutrino mass matrix:

Neutrino mixing matrix in the FL model Tri-bimaximal mixing pattern b=c, exact mu-tau symmetry In the limit Generalized to the CP violating case by inserting phase factor Note: neutrinos are Dirac particles in the FL model

Generalization of the FL model We aim to Dirac neutrino Majorana neutrino General CP violating case with all the parameters being complex Scenario A:

Neutrino mixing matrix in scenario A CP phases Mixing angles:

Neutrino masses in scenario A Only the normal mass hierarchy is allowed in scenario A

Scenario B Compared with scenario A, Dirac CP phase is vanishing and two Majorana phases are included. The mixing angles are the same as that in the FL model.

Scenario B Normal mass hierarchy Inverted mass hierarchy Both normal and inverted mass spectrums are allowed m0 can not be purely imaginary. a=b=c is not favored

× Scenario B a=b=c is not allowed Rho and sigma are less restricted in both normal and inverted cases

Generic analysis CP violating phases are less constrained

Generic formulae of masses and Majorana CP phases More freedom to fit exp data Can be tested in the future more precise experiment

Summary Tri-Bi θcorrection CP phase The nearly tri-bimaximal mixing pattern can be regarded as a natural consequence of the slight mu-tau symmetry breaking in the FL model Tri-Bi θcorrection CP phase Both scenario A and scenario B are compatible with current experimental data

The maximum of the atmospheric mixing angle may survive the mu-tau symmetry breaking A possible way to generate slight mu-tau symmetry breaking, radiative correction: renormalization group equation evolution, threshold effect… … GUT N EW full theory effective theory S. Luo, J.W. Mei and Z.Z. Xing, PRD 72(2005)053014

Thanks