1. Democratic (s)fermions and lepton flavor violation Mitsuru Kakizaki (ICRR, University of Tokyo) June 18, 2004 Ref.: K. Hamaguchi, M. K. and Masahiro Yamaguchi, PRD68 (2003) 056007 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) Mitsuru Kakizaki

2. 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 Mitsuru Kakizaki

3. Attempts to solve SUSY flavor problem • Fermion and sfermion mass puzzles are simultaneously solved • Measurement of FCNC processes and sfermion mass spectra Fermion mass generation mechanism may be revealed 1. Degeneracy: 2. Alignment: without degeneracy Thistalk Idea：　High energy theory which controls flavor SUSY FCNC suppression Fermion masses and mixing Interesting points of alignment: Mitsuru Kakizaki

4. 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) Mitsuru Kakizaki

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

6. sym. Neutrino mass matrix • Consider Majorana neutrinos: Universal Democratic • Here we take universal mass term: Degenerate neutrinos；Bi-large mixing, small • Small angles in the quark sector: Mitsuru Kakizaki

7. New 3. Democratic sfermions [Hamaguchi--M. K.--Yamaguchi (2002)] Idea： Interactions between SUSY SM fields and hidden fields are also democratic • Kahler potential （Bilinear part of ）： Hidden fields • Soft sfermion mass matrix: 3rd generation sfermion mass differs from first two generation masses Mitsuru Kakizaki

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

9. 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 Mitsuru Kakizaki

10. Experimental bound: Foreseeable future: • Prediction of democratic model：　（For small 　　　 ）　 [MEGA (1999)] [MEG@PSI] Mitsuru Kakizaki

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

12. 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 Mitsuru Kakizaki

13. SUSY SM + right-handed neutrinos (mSUGRA + RG effects) Collider experiments: LFV searches: Democratic model （Generation mixing without RG effects） New 4. Comparison between mSUGRA and democratic model [Moroi(1994)] LHC, polarized muon may distinguish models of SUSY [Kuno—Okada(1996)] Mitsuru Kakizaki

14. 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 Mitsuru Kakizaki

15. Backup slides Mitsuru Kakizaki

16. For large Mitsuru Kakizaki

17. 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 Mitsuru Kakizaki

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

19. 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 generationsdoubletsFCNC suppression Small mixing in the lepton sector × Mitsuru Kakizaki

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

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

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

23. 199Hg EDM • CP violating interaction: T violating nuclear force: Interaction between nuclear and ： Spin of nuclear EDM of 199Hg atom Mitsuru Kakizaki

24. Group theoretical interpretation • Charged lepton mass matrix sym. broken by vevs: Hierarchical mass spectrum: Same result as the case of democratic + diagonal breaking Mitsuru Kakizaki

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

26. 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: Mitsuru Kakizaki

27. breaking in sfermion mass terms • Here we introduce new parity symmetry: Doublets: -- Singlets: + • Yukawa structure is NOT modified • Sfermion mass matrix: Magnitude of sfermion mixing is same as the case without breaking Mitsuru Kakizaki

28. Scalar trilinear coupling （A-term） Source of Left-Right mixing • In superCKM basis Small generation mixing Alignment is realized Mitsuru Kakizaki

29. LFV decay of • Prediction of democratic model • Present upper bound: Mitsuru Kakizaki

30. transition SUSY GUT + （mSUGRA + RG effects） Democratic model • Squark mixing (real) • Sizable contribution to • Due to mixing CP asym. in • 199Hg EDM is dangerous • 199Hg EDM can be avoided Mitsuru Kakizaki

31. 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)] Mitsuru Kakizaki

32. Refs.: • K. Hamaguchi, M. K. and M. Yamaguchi, “Democratic (s)fermions and lepton flavorviolation,’’ 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]. Mitsuru Kakizaki