1. Oct. 25, 2004Mitsuru Kakizaki1 Flavor structure in supersymmetric models Mitsuru Kakizaki (ICRR, University of Tokyo) Oct. 25, 2004 @ Ochanomizu University We proposed a new alignment mechanism to solve the SUSY flavor problem We proposed a new alignment mechanism to solve the SUSY flavor problem Construction of a new alignment mechanism Comparison between the alignment mechanism and mSUGRA (degenerate sfermions)

2. Oct. 25, 2004Mitsuru Kakizaki2 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,’’ PLB594 (2004) 205.

3. Oct. 25, 2004Mitsuru Kakizaki3 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

4. Oct. 25, 2004Mitsuru Kakizaki4 2. Flavor problem of (soft) sfermion masses generation (tilde: superpartner) Viable solution to the hierarchy problem FermionBoson Supersymmetry (SUSY) ： Quark Squark GauginoGauge boson e.g. Superparticles have not been discovered (Soft) SUSY breaking terms are required e.g. Soft sfermion mass terms: New flavor parameters are introduced

5. Oct. 25, 2004Mitsuru Kakizaki5 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 ： e.g. K meson mixing: c.f. FCNCs are suppressed by GIM mechanism in SM

6. Oct. 25, 2004Mitsuru Kakizaki6 Attempts to solve SUSY flavor problem 1.Degeneracy: e.g. 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

7. Oct. 25, 2004Mitsuru Kakizaki7 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

8. Oct. 25, 2004Mitsuru Kakizaki8 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 ×

9. Oct. 25, 2004Mitsuru Kakizaki9 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)

10. Oct. 25, 2004Mitsuru Kakizaki10 Contents 1.Motivation 2.Democratic mass matrix model 3.Democratic sfermions 4.Comparison between the mSUGRA and democratic model 5.Summary

11. Oct. 25, 2004Mitsuru Kakizaki11 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:

12. Oct. 25, 2004Mitsuru Kakizaki12 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.

13. Oct. 25, 2004Mitsuru Kakizaki13 Neutrino mass matrix Consider Majorana neutrinos: Here we take universal mass term: UniversalDemocratic sym. Degenerate neutrinos ； Bi-large mixing, small

14. Oct. 25, 2004Mitsuru Kakizaki14 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:

15. Oct. 25, 2004Mitsuru Kakizaki15 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

16. Oct. 25, 2004Mitsuru Kakizaki16 Soft sfermion mass matrix Masses of 3rd generation sfermions differ from those of 1,2 generations

17. Oct. 25, 2004Mitsuru Kakizaki17 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

18. Oct. 25, 2004Mitsuru Kakizaki18 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

19. Oct. 25, 2004Mitsuru Kakizaki19 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

20. Oct. 25, 2004Mitsuru Kakizaki20 Experimental bound: Foreseeable future: Prediction of democratic model ： （ For small ） Branching ratio of LFV decay [MEGA (1999)] [MEG@PSI]

21. Oct. 25, 2004Mitsuru Kakizaki21 Branching ratio of LFV decay For large

22. Oct. 25, 2004Mitsuru Kakizaki22 CP violating squark mixing [Hisano--Shimizu(2003,2004)] Experimental bounds Democratic model When breaking parameters have CP phases of,, hadronic EDMs are dangerous hadronic EDMs: : For

23. Oct. 25, 2004Mitsuru Kakizaki23 Democratic model embedded in SU(5) GUT is promising SU(5): Universal masses of right-handed sdowns and left-handed sleptons is required by bi-large neutrino mixing Democratic model embedded in SU(5) GUT is promising SU(5): Universal masses of right-handed sdowns and left-handed sleptons is required by bi-large neutrino mixing Solution to CP violating FCNC problem In the absence of Left-Left or Right-Right mixing, CP violating squark generation mixing are suppressed

24. Oct. 25, 2004Mitsuru Kakizaki24 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(1996)]

25. Oct. 25, 2004Mitsuru Kakizaki25 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

26. Oct. 25, 2004Mitsuru Kakizaki26 Backup slides

27. Oct. 25, 2004Mitsuru Kakizaki27 Experimental constraint on 199 Hg EDM induced by chargino—up-type squark loop Constraint on CP violating mixing [Endo--M.K.--Yamaguchi(2003)] × ××

28. Oct. 25, 2004Mitsuru Kakizaki28 199 Hg EDM CP violating interaction: T violating nuclear force: Interaction between nuclear and ： Spin of nuclear EDM of 199 Hg atom

29. Oct. 25, 2004Mitsuru Kakizaki29 Group theoretical interpretation Charged lepton mass matrix sym. broken by the following vevs: Hierarchical mass spectrum: Same results as the case of democratic + diagonal breaking

30. Oct. 25, 2004Mitsuru Kakizaki30 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

31. Oct. 25, 2004Mitsuru Kakizaki31 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:

32. Oct. 25, 2004Mitsuru Kakizaki32 Magnitude of sfermion mixing is same order as the case without breaking breaking in sfermion mass terms Yukawa structure is NOT modified Resultant sfermion mass matrix: Here we introduce new parity symmetry: Doublets: --Singlets: + Assignment:

33. Oct. 25, 2004Mitsuru Kakizaki33 Scalar trilinear coupling （ A-term ） Source of Left-Right mixing Alignment is realized In superCKM basis Small generation mixing

34. Oct. 25, 2004Mitsuru Kakizaki34 LFV decay of Prediction of democratic model Present upper bound of implies c.f. Challenging for super B factories [Belle(2003)]

35. Oct. 25, 2004Mitsuru Kakizaki35 transition Large hadronic EDM can be avoided Hadrnic EDM is dangerous SUSY GUT + （ mSUGRA + RG effects ） Democratic model Squark mixing (real) mixing CP asym. in mixing

36. Oct. 25, 2004Mitsuru Kakizaki36 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)]