1 SUSY breaking studies Yasuhiro Okada (KEK) December 18, 2006 BNMII, Nara Women’s Univ.

2 New physics search at Super B factory Progress in understanding the electroweak symmetry breaking physics is expected in the LHC era. Electroweak symmetry breaking requires dynamics beyond three known gauge interactions, so that we expect something new at the TeV scale. Effects of new physics may appear in flavor physics observables. In order to distinguish various models, we need to study pattern of the deviations from the standard model predictions in many observables. Advantage of the planned super B factory is that there are several qualitatively different observables. For new physics search, correlations among quark flavor physics, lepton flavor physics and flavor-diagonal CP violation become important.

3 SUSY in Super B factory era LHC experiments will be a crucial test for existence of SUSY. (Squark/gluino mass reach ~ 2 -3TeV, A light Higgs boson) Mass spectrum from LHC and ILC will provide a hint for a SUSY breaking scenario. G.A.Blair, W.Porod, and P.M. Zerwas

4 Role of Flavor Physics Determine flavor structure of squark mass matrices. (New flavor mixing and new CP phases.) Quark mass -> Yukawa coupling Squark mass -> SUSY breaking terms SUSY breaking terms depend on SUSY breaking mechanism and interaction at the GUT/Planck scale. Diagonal tem: LHC/LC Off diagonal term: Flavor Physics

5 B physics in three SUSY models T.Goto, Y.O. Y.Shimizu, T.Shindou, and M.Tanaka, 2002,2003 and Super KEKB LoI In order to illustrate a potential of B physics in exploring flavor structure of SUSY breaking, we calculate various observables in three SUSY models. Models 1. Minimal supergravity model 2. SU(5) SUSY GUT with right-handed neutrino 3.MSSM with U(2) flavor symmetry Observables Bd-Bd mixing, Bs-Bs mixing. CP violation in K-K mixing (  ). Time-dependent CP violation in B ->J/  Ks, B->  Ks, B->K* . Direct CP violation in b->s .

6 Minimal supergravity model All squarks are degenerate at the Planck scale. Flavor mixings and mass-splittings are induced by renormalization. Flavor mixing in the d L sector. As a consequence, The CKM matrix is the only source of flavor mixing. SUSY CP phases (A-term,  term) constrained by EDM experiments. S.Belrolini, F.Borzumati, A.Masiero, and G.Ridorfi, 1991, …..

7 SU(5) SUSY GUT with right-handed neutrino Large flavor mixing in the neutrino sector can be a source of flavor mixing in the right- handed sdown sector. Correlation with LFV processes (  e , etc) is important. New CP phases in the GUT embedding. (T.Moroi) S.Baek,T.Goto,Y.O, K.Okumura, 2000,2001;T.Moroi,2000; N.Aakama, Y.Kiyo, S.Komine, and T.Moroi, 2001, D.Chang, A.Masiero, H.Murayama,2002; J.Hisano and Y.Shimizu, 2003;….

8 The LFV constraint depends on neutrino parameters Neutrino mass LFV mass terms for slepton (and sdown). Two cases considered for M R. (1)Degenerate case (M R ) ij = M  ij  Severe  >e  constraint (2) Non-degenerate case  ->e  suppressed (Casas and Ibarra, Ellis-Hisano-Raidal-Shimizu)

9 MSSM with U(2) flavor symmetry The quark Yukawa couplings and the squark mass terms are governed by the same flavor symmetry. 1st and 2nd generation => U(2) doublet 3rd generation => U(2) singlet A.Pomarol and D.Tommasini, 1996; R.Barbieri,G.Dvali, and L.Hall, 1996; R.Barbieri and L.Hall; R.Barbieri, L.Hall, S.Raby, and A.Romonino; R.Barbieri,L.Hall, and A.Romanino 1997; A.Masiero,M.Piai, and A.Romanino, and L.Silvestrini,2001; ….

10 A(B->J/  Ks)   m(Bs)/  m(Bd) mSUGRA SU(5) GUT Degenerate SU(5) GUT Non-degenerate U(2) FS Small deviation in mSUGRA. Bd unitarity triangle is closed, but  K has a large SUSY contribution in SU(5) GUT for the degenerate M R case. Bs mixing receives SUSY effects for the non-degenerate case. Various SUSY contributions for the U(2)flavor symmetry model. Unitarity triangle

11 CP asymmetries in B  Ks and b  s  Direct asymmetry in b  s  CP asymmetry in B  Ks CP asymmetry in B  K* 

12 Update 2006 (preliminary results) We have taken into account the new measurement of the Bs mixing. (CDF) Many technical improvements concerning radiative corrections at the SUSY scale. T.Goto, Y.O., T.Shindou, and M.Tanaka

13 Unitarity triangle The Bs mixing constraint is strong. Survival points are reduced due to a slight tension between |Vub| and sin2  1 measurements SU(5) GUT Degenerate SU(5) GUT Non-degenerate U(2) FS

14 Difference between the Bd mixing angle and real 2  1 :U(2) case Need to determine |Vub| and  3 at a few % level to distinguish this difference.

15 S(  Ks)-S(J/  Ks) SU(5) GUT Degenerate SU(5) GUT Non-degenerate Difference can be % for SU(5) GUT with non-degenerate case and the U(2) model. U(2) FS

16 Direct and mixing induce asymmetry in b to s  CP asymmetry in B  K*  Direct asymmetry in b  s  A few% % SU(5) GUT Degenerate SU(5) GUT Non-degenerate U(2) FS

17 CP violating phase in the Bs mixing S(Bs->J/  ) can deviate from the SM by 5-10% for SU(5) GUT with non-degenerate case and the U(2) model. SU(5) GUT Degenerate SU(5) GUT Non-degenerate U(2) FS

18 Tau and muon lepton flavor violation LFVs are processes that limit the parameter space. SU(5) GUT Degenerate SU(5) GUT Non-degenerate U(2) FS  ->e  ->e  and  -> 

19 Electric dipole moments Neutron and Hg electric dipole moments are other important limiting processes. Although theoretical uncertainty is still large, EDM is a promising signal for models of 2-3 mixing of right-handed squark. Stronger constraints are obtained if we use the estimation of the neutron EDM from the strange quark chromomagentic moment in the chiral perturbation theory (J. Hsano and Y. Shimizu, 2004). U(2) FSSU(5) GUT Non-degenerate

20 Bd- unitarity Triangle test T-dep CPV in B->  Ks, B->K*  b->s  direct CP T-dep CPV in Bs->J/  LFVEDM mSUGRA _ _____ SU(5)SUSY GUT + R (degenerate) _ ___  ->e  _ SU(5)SUSY GUT + R (non-degenerate) _ <O(10%) _ <~5%  ->e   ->  nEDM U(2) Flavor symmetry < a few % <O(10%) < a few % <~5%  ->e   >  nEDM Summary of possible deviations from the SM prediction

21 Summary We have updated the study of the flavor signals in three SUSY models. The measurement of the Bs mixing have already put strong constraints on possible deviations especially for b-s transition processes. Although the pattern of the deviations is similar to the previous case, numerical values are somewhat more constrained. Quark flavor signals, Lepton flavor violation and EDM are correlated differently for each case, so that improvements in all processes are important.