1. May 25, 2004Kakizaki, Mitsuru1 Flavor structure in supersymmetric models Kakizaki, Mitsuru (ICRR, University of Tokyo) May 25, 2004 We proposed a new alignment mechanism to solve SUSY flavor problem We proposed a new alignment mechanism to solve SUSY flavor problem Construction of a new alignment mechanism Comparison between the alignment mechanism and mSUGRA (degenerate sfermions) Ref.: K. Hamaguchi, M. K. and Masahiro Yamaguchi, “Democratic (s)fermions and lepton flavor violation,’’ PRD68 (2003) 056007

2. May 25, 2004Kakizaki, Mitsuru2 １． Motivation 1. Fermion masses and mixing in the standard model (with neutrino mass terms) Hierarchy in charged fermion masses ： Small generation mixing in the quark sector ： Large mixing in the lepton sector ： Two severe flavor puzzles in SUSY models

3. May 25, 2004Kakizaki, Mitsuru3 2. Flavor problem of (soft) sfermion masses Supersymmetry (SUSY) ： Fermion Boson ex.) Quark Squark Gaugino Gauge boson ： superpartner Superparticles have not been discovered SUSY must be broken (Soft) SUSY breaking terms are required ex. ) Soft sfermion mass terms: generation

4. May 25, 2004Kakizaki, Mitsuru4 Generic sfermion masses and mixing Unacceptably large flavor changing neutral currents (FCNCs) Generic sfermion masses and mixing Unacceptably large flavor changing neutral currents (FCNCs) SUSY flavor problem Constraint ： ex.) K meson mixing:

5. May 25, 2004Kakizaki, Mitsuru5 Attempts to solve SUSY flavor problem 1.Degeneracy: ex. ) mSUGRA: Sfermion masses arise in flavor blind manner at a high energy scale Generation mixing is induced only by RG effects SUSY flavor problem is solved 2.Alignment: Today’s talk

6. May 25, 2004Kakizaki, Mitsuru6 Idea ： High energy theory which controls flavor SUSY FCNC suppression Fermion masses and mixing Idea ： High energy theory which controls flavor SUSY FCNC suppression Fermion masses and mixing Alignment ： Interesting points ： Fermion and sfermion mass puzzles are simultaneously solved Measurement of FCNC processes and sfermion mass spectra Fermion mass generation mechanism may be revealed [Nir--Seiberg(1993)] Fermion and sfermion squared mass matrices are aligned in field space simultaneously diagonalized

7. May 25, 2004Kakizaki, Mitsuru7 Weak points of characteristic alignment mechanisms U(1) flavor symmetry (Abelian) ： [Nir — Seiberg (1993)] Many U(1) flavor symmetries are necessary for adequate FCNC suppression × U(2) flavor symmetry (Non-Abelian) ： [Barbieri — Hall — Raby — Romanino (1997)] 1, 2 generations doublets FCNC suppression Small mixing in the lepton sector ×

8. May 25, 2004Kakizaki, Mitsuru8 Purpose Proposal of a new alignment mechanism based on the democratic mass matrix model, which explains neutrino bi-large mixing Comparison between this alignment mechanism and conventional mSUGRA ： Mass spectra of sfermions Charged lepton flavor violation (LFV)

9. May 25, 2004Kakizaki, Mitsuru9 Contents 1.Motivation 2.Democratic mass matrix model 3.Democratic sfermions 4.Comparison between the mSUGRA and democratic model 5.Summary

10. May 25, 2004Kakizaki, Mitsuru10 Idea: Equality of three generations 2. Democratic mass matrix model [Harari—Haut--Weyers (1978); Koide (1983, 1989); Fritzsch--Xing (1995); Fukugita—Tanimoto--Yanagida(1998)] 3 = 1 + 2 Permutation group on 3 objects: : 3-dim. reducible rep. 3rd generations:

11. May 25, 2004Kakizaki, Mitsuru11 Charged lepton mass matrix Unique invariant Small breaking Democratic mass matrix: Hierarchical mass spectra: Bi-large unitary matrix: Small angles in the quark sector: sym.

12. May 25, 2004Kakizaki, Mitsuru12 Neutrino mass matrix Consider Majorana neutrinos: Here we take universal mass term: UniversalDemocratic sym. Degenerate neutrinos ； Bi-large mixing, small

13. May 25, 2004Kakizaki, Mitsuru13 Comparison between U(2) and democratic （ 1,2 generations ～ Doublets, ３ rd generations ～ Singlets ） Differences in neutrino mass matrix U(2) No symmetric singlet Small mixing × Democratic Large mixing arises from breaking terms （ In the basis of diagonal charged lepton mass matrix ） Universal masses are allowed:

14. May 25, 2004Kakizaki, Mitsuru14 Idea ： Interactions between SUSY SM fields and hidden fields are also democratic Idea ： Interactions between SUSY SM fields and hidden fields are also democratic 3. Democratic sfermions Universal Democratic [Hamaguchi--M. K.--Yamaguchi (2002)] Kahler potential （ Bilinear part of ）： Functions of (hidden) fields

15. May 25, 2004Kakizaki, Mitsuru15 Soft sfermion mass matrix Masses of 3rd generation sfermions differ from those of 1,2 generations

16. May 25, 2004Kakizaki, Mitsuru16 Democratic model solves SUSY flavor problem Squark generation mixing: Small generation mixing without universality Alignment is realized Masses of 1,2 generation sfermions are degenerate 1-2 mixing is extremely suppressed Suppression of SUSY contributions to FCNCs

17. May 25, 2004Kakizaki, Mitsuru17 Properties of democratic model Predictions of lepton sector Slepton mass spectra LFV decay CP violating squark generation mixing Experimental bounds and estimation in democratic model Solution to CP violating squark generation mixing

18. May 25, 2004Kakizaki, Mitsuru18 Slepton masses Left-handed slepton mass spectrum Presence of democratic part in Kahler potential for Democratic part in neutrino mass matrix in canonical basis × Bi-large neutrino mixing requires universal form for Kahler potential for : Left-Left mixing vanishes Right-handed slepton mass spectrum Small Right-Right mixing

19. May 25, 2004Kakizaki, Mitsuru19 Experimental bound: Foreseeable future: Prediction of democratic model ： （ For small ） LFV decay [MEGA (1999)] [MEG@PSI]

20. May 25, 2004Kakizaki, Mitsuru20 LFV decay For large

21. May 25, 2004Kakizaki, Mitsuru21 CP violating squark mixing [Endo--M.K.--Yamaguchi(2003)] [Hisano--Shimizu(2003)] Experimental bounds Democratic model When breaking parameters have CP phases of,, 199 Hg EDM are dangerous 199 Hg EDM

22. May 25, 2004Kakizaki, Mitsuru22 Solution to CP violating FCNC problem In the absence of Left-Left or Right-Right mixing CP violating squark generation mixing are suppressed Democratic model embedded in SU(5) GUT SU(5): Universal masses of right-handed sdowns and left-handed sleptons is required by bi-large neutrino mixing

23. May 25, 2004Kakizaki, Mitsuru23 4. Comparison between mSUGRA and democratic model SUSY SM + right-handed neutrinos (mSUGRA + RG effects) Collider experiments: LFV searches: Democratic model （ Generation mixing without RG effects ） LHC, polarized muon may distinguish models [Kuno—Okada]

24. May 25, 2004Kakizaki, Mitsuru24 5. Summary One interesting solution to SUSY flavor problem: The mechanism which dictates fermion mass structure also suppresses FCNCs Alignment We proposed a new successful alignment mechanism based on the democratic mass matrix model Predictions of the democratic model differ form those of mSUGRA Observable

25. May 25, 2004Kakizaki, Mitsuru25 Backup slides

26. May 25, 2004Kakizaki, Mitsuru26 Experimental constraint on 199 Hg EDM induced by chargino—up-type squark loop Constraint on CP violating mixing [Endo--M.K.--Yamaguchi(2003)] × ××

27. May 25, 2004Kakizaki, Mitsuru27 199 Hg EDM CP violating interaction: T violating nuclear force: Interaction between nuclear and ： Spin of nuclear EDM of 199 Hg atom

28. May 25, 2004Kakizaki, Mitsuru28 Group theoretical interpretation Charged lepton mass matrix sym. broken by vevs Hierarchical mass spectrum: Same result as the case of democratic + diagonal breaking

29. May 25, 2004Kakizaki, Mitsuru29 Neutrino masses generated by seesaw mechanism Dirac, heavy neutrino mass matrix: Light neutrino mass matrix: Assume that right-handed neutrinos transform as triplet under and take universal matrix [Fujii--Hamaguchi--Yanagida(2002)] Degenerate light neutrino masses

30. May 25, 2004Kakizaki, Mitsuru30 Slepton mixing in mSUGRA mSUGRA + Right-handed neutrinos + Seesaw Slepton masses arise in flavor blind manner at a high energy scale: at Heavy right-handed neutrinos have flavor changing Yukawa couplings Left-handed slepton mixing is induced by RG effects:

31. May 25, 2004Kakizaki, Mitsuru31 Magnitude of sfermion mixing is same as the case without breaking breaking in sfermion mass terms Yukawa structure is NOT modified Sfermion mass matrix: Here we introduce new parity symmetry: Doublets: --Singlets: +

32. May 25, 2004Kakizaki, Mitsuru32 Scalar trilinear coupling （ A-term ） Source of Left-Right mixing Alignment is realized In superCKM basis Small generation mixing

33. May 25, 2004Kakizaki, Mitsuru33 LFV decay of Prediction of democratic model Present upper bound:

34. May 25, 2004Kakizaki, Mitsuru34 transition 199 Hg EDM can be avoided 199 Hg EDM is dangerous SUSY GUT + （ mSUGRA + RG effects ） Democratic model Squark mixing (real) Sizable contribution to Due tomixing CP asym. in

35. May 25, 2004Kakizaki, Mitsuru35 Problems of democratic model Absence of physical motivations What is the origin of the democratic mass matrix? Symmetry Geometry What is the origin of the small breaking? Why is the democratic part absent for ? [Watari—Yanagida(2002)]

36. May 25, 2004Kakizaki, Mitsuru36 Refs.: K. Hamaguchi, M. K. and M. Yamaguchi, “Democratic (s)fermions and lepton flavor violation,’’ PRD68 (2003) 056007; M. Endo, M.K. and M. Yamaguchi, “New constraint on squark flavor mixing from Hg-199 electric dipole moment,’’ PLB583 (2004) 186; M. Endo, M.K. and M. Yamaguchi, “Large supersymmetric contribution to CP asymmetry of from left-handed squark mixing,’’ To appear in PLB [hep-ph/0403260].