1. June 18, 2004Mitsuru Kakizaki1 Democratic (s)fermions and lepton flavor violation Mitsuru Kakizaki (ICRR, University of Tokyo) June 18, 2004 We propose a new alignment mechanism to solve SUSY flavor problem We propose 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, PRD68 (2003) 056007

2. June 18, 2004Mitsuru Kakizaki2 １． Motivation Two severe flavor puzzles in SUSY models 1. Fermion masses and mixing Large mass hierarchy among charged fermions Small quark mixing Large lepton mixing 2. SUSY flavor problem Generic sfermion masses and mixing Unacceptably large FCNC processes Experimental constraints: for

3. June 18, 2004Mitsuru Kakizaki3 Attempts to solve SUSY flavor problem 1. Degeneracy: 2. Alignment:without degeneracy 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 Fermion and sfermion mass puzzles are simultaneously solved Measurement of FCNC processes and sfermion mass spectra Fermion mass generation mechanism may be revealed Interesting points of alignment: This talk

4. June 18, 2004Mitsuru Kakizaki4 Purpose Proposal of a new alignment mechanism based on the democratic mass matrix model, which explains neutrino bi-large mixing Comparison between the alignment mechanism and conventional mSUGRA ： Mass spectra of sfermions Charged lepton flavor violation (LFV)

5. June 18, 2004Mitsuru Kakizaki5 Unique invariantSmall breaking Democratic mass matrix: Bi-large unitary matrix: sym. Charged lepton mass matrix Hierarchical mass spectra: Idea: Equality of three generations 2. Democratic mass matrix model [Harari—Haut--Weyers (1978); Koide (1983, 1989); Fritzsch--Xing (1995); Fukugita—Tanimoto--Yanagida(1998)]

6. June 18, 2004Mitsuru Kakizaki6 Neutrino mass matrix Consider Majorana neutrinos: Here we take universal mass term: UniversalDemocratic sym. Degenerate neutrinos ； Bi-large mixing, small Small angles in the quark sector:

7. June 18, 2004Mitsuru Kakizaki7 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 [Hamaguchi--M. K.--Yamaguchi (2002)] Kahler potential （ Bilinear part of ）： 3rd generation sfermion mass differs from first two generation masses Hidden fields Soft sfermion mass matrix:

8. June 18, 2004Mitsuru Kakizaki8 Sfermion mass matrix in the superCKM basis: Small generation mixing without universality Alignment is realized SUSY contributions to FCNCs are suppressed Democratic model solves SUSY flavor problem Sfermion mixing

9. June 18, 2004Mitsuru Kakizaki9 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

10. June 18, 2004Mitsuru Kakizaki10 Experimental bound: Foreseeable future: Prediction of democratic model ： （ For small ） [MEGA (1999)] [MEG@PSI]

11. June 18, 2004Mitsuru Kakizaki11 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

12. June 18, 2004Mitsuru Kakizaki12 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

13. June 18, 2004Mitsuru Kakizaki13 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 of SUSY [Kuno—Okada(1996)] [Moroi(1994)]

14. June 18, 2004Mitsuru Kakizaki14 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 from those of mSUGRA Observable

15. June 18, 2004Mitsuru Kakizaki15 Backup slides

16. June 18, 2004Mitsuru Kakizaki16 For large

17. June 18, 2004Mitsuru Kakizaki17 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. June 18, 2004Mitsuru Kakizaki18 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:

19. June 18, 2004Mitsuru Kakizaki19 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 ×

20. June 18, 2004Mitsuru Kakizaki20 Soft sfermion mass matrix Masses of 3rd generation sfermions differ from those of 1,2 generations

21. June 18, 2004Mitsuru Kakizaki21 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:

22. June 18, 2004Mitsuru Kakizaki22 Experimental constraint on 199 Hg EDM induced by chargino—up-type squark loop Constraint on CP violating mixing [Endo--M.K.--Yamaguchi(2003)] × ××

23. June 18, 2004Mitsuru Kakizaki23 199 Hg EDM CP violating interaction: T violating nuclear force: Interaction between nuclear and ： Spin of nuclear EDM of 199 Hg atom

24. June 18, 2004Mitsuru Kakizaki24 Group theoretical interpretation Charged lepton mass matrix sym. broken by vevs: Hierarchical mass spectrum: Same result as the case of democratic + diagonal breaking

25. June 18, 2004Mitsuru Kakizaki25 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

26. June 18, 2004Mitsuru Kakizaki26 Slepton mixing in mSUGRA MSSM + Right-handed neutrinos + mSUGRA 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:

27. June 18, 2004Mitsuru Kakizaki27 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: +

28. June 18, 2004Mitsuru Kakizaki28 Scalar trilinear coupling （ A-term ） Source of Left-Right mixing Alignment is realized In superCKM basis Small generation mixing

29. June 18, 2004Mitsuru Kakizaki29 LFV decay of Prediction of democratic model Present upper bound:

30. June 18, 2004Mitsuru Kakizaki30 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

31. June 18, 2004Mitsuru Kakizaki31 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)]

32. June 18, 2004Mitsuru Kakizaki32 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].