1. 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/ , Phys. Lett. B 641(2006)189

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

3. ? 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/

4. 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?

5. 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.

6. 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) S4
S3×Z2, D4 … …
E. Ma, PLB 632(2006)352

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

8. 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

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

10. Neutrino mixing matrix in scenario A
CP phases
Mixing
angles:

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

12. 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.

13. 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

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

15. Generic analysis
CP violating phases are less constrained

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

17. 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

18. 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

19. Thanks