Twisted Flavors and Tri-bimaximal Neutrino Mixing

1. Twisted Flavors and Tri-bimaximal Neutrino Mixing Phys.Rev.Lett.97,041601,2006 arXiv:hep-ph/0603116 Atsushi Watanabe (Kyushu U. ) with Koichi Yoshioka (Kyushu U.), Naoyuki Haba (Tokushima U. & Munich, Tech. U.) 28/09/2006 @DESY

2. Contents • Introduction • Scherk-Schwarz flavor twisting • Tri-bimaximal neutrino mixing • Summary Flavor symmetry breaking by the boundary conditions on the extra dimension realistic neutrino mixings

3. Introduction • Lepton flavor mixing (3 generations) [M.C.Gonzalez-Garcia, C.Pena-Garay,’03;A.Bandyopadhyay, S.Choubey, S.Goswami, S.T. Petcov, D.P. Roy,’05] breaking flavor symmetry observables

4. Symmetry breaking • Vacuum expectation values of scalar fields • Structure of extra-dimensional space

5. Compactification Scherk-Schwarz compactification [Scherk and Schwarz,’79] translation: identification of points:

6. Orbifolding reflection: Boundary conditions are

7. Neutrino flavor twisting • 5-dim model (for simplicity) • 5-dim Dirac fermion (gauge singlet) • Other fields are confined on 4-dim 4-dim [K.Dienes, E.Dudas, T.Gherghetta,’99]

8. 2 1 3 Flavor symmetry • permutation group • A simple non-abelian discrete group [S.Pakvasa, H.Sugawara,’78; H.Harari, H.Haut, J.Weyers,’78]

10. Lagrangian the mode expansion of integrating over integrating out the infinite tower of bulk neutrinos

11. Mass matrix of left-handed neutrino eigenvalues eigenvectors

12. Mass spectrum Inverted hierarchy or degenerate Typical mass scale

13. bulk Majorana mass boundary Dirac mass Comment on the mass eigenvalues ordinary seesaw conventional behavior

14. Mixing angles for neutrinos “tri-bimaximal mixing” [P.F. Harrison, D.H. Perkins, W.G. Scott,’02]

15. symmetry breaking , in order to produce In general, １．　Large symmetry breaking term ２．A special type of symmetry breaking the last term is not general form of

16. Summary • We utilize Scherk-Schwarz twist for handling flavor symmetry breaking. • Assuming as a flavor symmetry for neutrino sector, light neutrino phenomenology has rich and robust predictions such as tri-bimaximal mixing form of generation mixing. quark sector, GUT, phenomenology, …

17. This boundary condition corresponds to two parities on and

18. small

19. triplet Charged-lepton sector small mixing for left-handed direction

20. この操作は に関する折り返しになっている と定義すると 先ほどの は 両方で non-trivial　にひねってみると..

21. Consistency conditions is a parity Furthermore, and must satisfy

22. : Possible boundary conditions e.g. from

23. Possible boundary conditions