Quark and Lepton Mixing in S 4 Flavor Model

1. Quark and Lepton Mixing inS4 Flavor Model September 28, 2010 Max-Planck-Institut für Kernphysik Heidelberg, Germany Morimitsu Tanimoto (Niigata University) with H. Ishimori and Y. Shimizu

2. Niigata ↓

3. Niigata City Population:811,996 Niigata City is an urban center developed by its port. Even though it is located on a substantial expansion of agricultural landscapes, it has also easy accesses to major cities by airplanes, express omnibuses, and bullet trains. Also from its international airport, there are regular flights to Harbin, Shanghai, Seoul, Vladivostok, Khabarovsk, Guam. Niigata aspires to be a gateway to the East Asia. Niigata University Niigata University

4. Plan of my talk 1 Tri-bi maximal mixing and Flavor Symmetry 2 S4 Flavor Model in Quarks and Leptons 3 S4 Flavor Model in Sleptons 4 Summary

5. 1 Tri-bimaximal mixing and Flavor symmetry Recent experiments of the neutrino oscillations go into a new phase of precise determination of mixing angles and mass squared differences. Three Flavor analysis strongly suggests Tri-bimaximal Mixingof Neutrinos Harrison, Perkins, Scott (2002) indicates Non-Abelian Flavor Symmetry ?

6. Consider the structure of Neutrino Mass Matrix, which gives Tri-bi maximal mixing Mixing angles are independent of mass eigenvalues Different from quark mixing angles

7. Quark Sector 7

8. Let us consider Flavor Symmetry. 8

9. × Need some ideas to realize Tri-bi maximal mixing by S3 flavor symmetry

10. A4 Symmetry may be hidden. triplet(νe,νμ,ντ)L ○ 3L×3L×3H 3L×3L A4 should be broken ! T’ , S4 , Δ(54)flavor models also give Tri-bi maximal mixing !

11. Δ（27）,Δ（54）,Σ（81）

12. Origin of the non-Abelian Flavor symmetry ? Tri-bimaximal neutrino mixing from orbifolding, G.Altarelli, F.Feruglio, Y.Lin, NPB775, 31 (2007) hep-ph/0610165 Stringy origin of non-Abelian discrete flavor symmetries T. Kobayashi, H. Niles, F. Ploeger, S. Raby, M. Ratz, NPB768,135(2007) hep-ph/0611020 Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models H. Abe, K-S. Choi, T. Kobayashi, H. Ohki, NPB820, 317 (2009) , 0904.2631 Non-Abelian Discrete Flavor Symmetry from T2/ZN OrbifoldsA.Adulpravitchai, A. Blum, M. Lindner, JHEP0907, 053 (2009), 0906.0468 Non-Abelian Discrete Groups from the Breaking of Continuous Flavor Symmetries A.Adulpravitchai, A. Blum, M. Lindner, JHEP0909, 018 (2009), 0907.2332

13. Reference Non-Abelian Discrete Symmetries in Particle Physics Hajime Ishimori, Tatsuo Kobayashi, Hiroshi Ohki, Hiroshi Okada, Yusuke Shimizu, Morimitsu Tanimoto, e-Print: arXiv:1003.3552[hep-th] Prog.Theor.Phys.Suppl.183:1-163,2010 We review pedagogically non-Abelian discrete groups and show some applications for physical aspects. This article includes a brief view on general aspects of group theory, i.e. something basic and useful theorems.

14. Flavor Symmetry of Neutrinos is related with Physical Phenomena. ●Ue3=0 in Tri-bimaximal mixing! There are hints Non-zero Ue3 in experiments. How can one predict Ue3 ? ●CKM mixing in Quarks ? Cabibbo angle? We need Quark-lepton unification in a GUT. ●SUSY Flavor Sector,SUSY FCNC , EDM We discuss the case of S4 symmetry.

15. Before discussing S4 model, let us understand how to get the tri-bimaximal mixing in the example of A4 flavor model. E. Ma and G. Rajasekaran, PRD64(2001)113012 Four irreducible representations in A4symmetry 1 1’ 1” 3

17. 3L × 3flavon → 1 3L × 3flavon → 1” 3L × 3flavon→ 1’ 3L × 3L → 1 3L × 3L× 3flavon → 1 1’ × 1” → 1

18. These mass matrices do not yet predict tri-bimaximal mixing ! Can one get Desired Vacuum in Spontaneous Symmetry Breaking ? Scalar Potential Analysis

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20. As seen in this A4 model, in order to reproduce the tri-bi maximal mixing, we need Non-Abelian Discrete Symmetry (A4, T’, S4… ) and Symmetry Breaking Vacuum Alignment of flavons. Spontaneous Breaking ? ( Scalar potential ) Explicit Breaking ? (Boundary condition in extra-dim.)

21. 2 S4 Flavor Model in Quarks and Leptons H. Ishimori, K. Saga, Y. Shimizu, M. Tanimoto, arXiv:1004.5004 S4×Z4 with SUSY SU(5) GUT⇒Tri-bimaximal, Cabibbo angle C.Hagedorn, M.Lindner, R.N.Mohapatra, JHEP 0606, 042 (2006) SO(10) B.Dutta, Y. Mimura, R.N. Mohapatra, arXiv:0911.2242 SO(10) C.Hagedorn, S. F. King, C. Luhn, arXiv:1003.4249 SU(5) R.d.A. Toorop, F. Bazzocchi, L. Merlo, arXiv: 1003.4502 Pati-Salam

22. S4×Z4×U(1)FN with SUSY SU(5) GUT Up quarks MR Dirac Neutrinos Charged leptons Down quarks We take l=m=1, n=2.

23. S4 invariant superpotential for leptons 3L×2R×3flavon 3L×1R×3flavon 1R×1R 2R×2R 2R×2R×2flavon 3L×2R×3flavon 3L×1R×3flavon

24. We take VEV’s We getLepton Mass Matrices ○ Due to m-n<0 ○ ○ ○

25. Vacuum alignment No mixing in the left-hand ! Θ12=60°in the right-hand !

26. After seesaw, we get the tri-bimaximal mixing

27. Deviation from the Tri-bimaximal mixing due to Higher dimensional mass operators Superpotential of next-to-leading order

28. The charged lepton mass matrix including the next-to-leading terms Since the lepton mixing is given as we have non-zero Ue3 0.003

29. Next-to-leading in Neutrino sector

30. Determination ofmagnitudes Desired Vacuum Alignments FNcharges l=m=1, n=2 Putting observed masses and M=1012 GeV, we get

31. We can predict mixing angles.

32. Quark Sector is predicted. Down Quarks Left-handed mixing is given as

33. Including next-to-leading order, we get

34. Up Quark Sector Direct Yukawa coupling We add the next-to-leading mass matrix

35. Up Quarks We take alignment , we get After rotating it by the orthogonal matrix, We obtain

36. We obtain CKM matrix elements In the leading order, we predict

37. Including next-to-leading order corrections, we get The parameter set reproduces observed values very well. Values of parameters are consistent with our mass matrices. CP violation can be discussed !

38. 3. S4 Flavor Symmetry in Sleptons Flavor symmetry constrains not only quark/lepton mass matrices, but also mass matrices of their superpartner, i.e. squark/slepton Specific patterns of squark/slepton mass matrices could be tested in future experiments. In this talk, we concentrate on lepton FCNC. Consider Soft SUSY Breaking Term in Supergravity.

39. Second order Slepton mass matrices are derived from

40. For the left-handed sector, higher dimensional terms are given as Left-handed Slepton mass matriｘ is

41. Right-handed Slepton mass matrix is

42. Move to Super-CKM basis (Diagonal Basis of Charged Lepton) in order to estimate magnitudes of FCNC. ○ Dominant term where Mass Insertion Parameters Experimental Constraint from μ→eγ F. Gabbiani, E. Gabrielli, A. Masiero and L. Silvestrini, Nucl. Phys. B477(1996) 321 Numerical analyses are required.

43. A terms are obtained as Dangerous ! Experimental Constraint We need numerical analyses of μ→eγ .

44. μ→eγDecay ○ ○ ○ ○

45. EDM of Electron ○ ○ J.Hisano, M. Nagai, P. Paradisi, Phys.Rev.D80:095014,2009.

46. Preliminary

47. Assume the maximal phase Assume the maximal phase

48. Assume the maximal phase

50. 4Summary ☆ S4 Flavor Symmetry in SU(5) can give realistic quark and lepton mixing matrices. Tri-bimaximal mixing, Cabibbo angle ☆ S4 discrete symmetries work to suppress FCNC in the framework of gravity mediation in SUSY breaking. ★ Squark sectors in S4 Symmetry ? ★ Origin of S4 Symmetry ? ★ Mass Spectrum ?