1. 1 SUSY in B decays Yasuhiro Okada (KEK) Super B factory workshop in Hawaii January 21, 2004, Honolulu

2. 2 New physics search at Super B factoory Various ways to look for new physics effects. Consistency of unitarty triangle. Comparison of CP asymmetry in B -> J/  Ks and B->  Ks. Direct and mixing-induced CP asymmetries of B -> Ms   Branching ratio and lepton FB asymmetries of b ->sll.  Branching ratio of B->D   Lepton flavor violation in tau decays. Not just to get a hint of physics beyond the Standard model, but distinguish different models from pattern of deviations from the SM of various observable quantities.

3. 3 SUSY in Super B factory era LHC experiments will be a crucial test for existence of SUSY. (Squark/gluino mass reach ~ 2 TeV, A light Higgs boson) Role of Super B factory is to determine the flavor structure of squark mass matrixes. (new sources of flavor mixing and CP phases) Squark mass matrixes carry information of SUSY breaking mechanism and interactions at high energy scale (ex. GUT/Planck scale). Diagonal tem: LHC/LC Off diagonal term: Flavor Physics

4. 4 Content of this talk Comparative study of SUSY effects in unitarity triangle and rare B decay in three SUSY models. B physics signals for benchmark cases (Snowmass Points and Slopes). 1. Minimal supergravity model 2. SU(5) SUSY GUT with right-handed neutrino 2-1. degenerate case 2-2. non-degenerate case 3. MSSM with U(2) flavor symmetry: T.Goto, Y.O. Y.Shimizu, T.Shindou, and M.Tanaka,

5. 5 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, …..

6. 6 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;….

7. 7 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)

8. 8 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; ….

9. 9 Numerical results We calculated SUSY effects to the following observables in the three models. CP violation in K-K mixing (  ). Bd-Bd mixing, Bs-Bs mixing. Mixing-induced CP violation in B ->J/  Ks, B->  Ks, B->Ms . Direct CP violation in b->s .

10. 10 Unitarity triangle mSUGRA SU(5) SUSY GUT with RHN A(B->J/  Ks)   Bs mixing mSUGRA : small deviation SU(5) Degenerate : 1-2 mixing SU(5) Non-degenerate : 2-3 mixing U(2) FS: large deviation 0.001200.5 Degenerate Non-degenerate U(2) FS

11. 11 CP asymmetry in B ->  Ks mode Hg EDM constraint included A(B->  Ks) A correlation between A(B->  Ks) and the s-quark EDM is pointed out. A constraint from the Hg EDM is strong. (J.Hisano and Y.Shimizu, 2003) Sizable deviation from the SM is possible in the non-degenerate case of SU(5) GUT and the MSSM with U(2) flavor symmetry.

12. 12 Mixing-induced and direct CP asymmetries in B -> Ms  Direct asymmetry in b -> s  Search for new phase in b-s transition. Mixing-induced asymmetry in B->Ms  Sensitive to b->s  R amplitude (ex. flavor mixing in the right-handed sdown sector)

13. 13 Deviation from the SM is at most 10% level for the mSUGRA model. In the SU(5) GUT with R, 1-2 flavor mixing is large for the degenerate case. -> Inconsistency between  and the B-triangle. 2-3 mixing signals for the non-degenerate case. -> Mixing induced CP asymmetries in B->  Ks, B->Ms  Various new physics signals for the MSSM with U(2) flavor symmetry.

14. 14 Bd- unitarity    m(Bs)B->  Ks B->Ms  indirect  CP b->s  direct CP mSUGRA closed SU(5)SUSY GUT + R (degenerate) closed SU(5)SUSY GUT + R (non-degenerate) closed U(2) Flavor symmetry large deviation sizable deviation small deviation Pattern of the deviation from the SM in various SUSY models. T.Goto,Y.Okada,Y.Shimizu, T.Shindo, and M.Tanaka

15. 15 Snowmass Points and Slopes (SPS) Benchmark points and model lines for SUSY studies mostly for LHC/LC. B.Allanach et al, Eur. Phys. J. C25, 113 (2002) We consider benchmark lines for the two cases of SU(5) GUT with RHN. Can B physics distinguish different models, even if the SUSY spectrum is the same as (similar to) the mSUGRA case? Diagonal term : Benchmark Off-diagonal term : GUT interaction Complementarity of LHC and Super B factory

16. 16 SPS is defined by mSUGRA inputs SPS 1a “SPS 1b” SPS 3 Typical points Coannihilation region Focus point SPS 2 SPS 3 SPS 1a SPS 1b SPS2 100 1000 0 M.Battaglia, et al, 2001 800 400 500

17. 17 Degenerate Non-degenerate A few % O(1) Deviation is small except for  K in the degenerate case of SPS2. T.Goto,Y.Okada,Y.Shimizu, T.Shindo, and M.Tanaka A few %  K and Bs mixing Input parameters. SUSY parameters : SPS Neutrino parameters: fixed (Hierarchical neutrino masses with MR~O(10^14) GeV) GUT phases: varied

18. 18 A(B->Ms  A(B->  Ks) Less than 1% A few % Rare decays with b->s transition Degenerate Non-degenerate Deviation is not so large even for the non- degenerate case. T.Goto,Y.Okada,Y.Shimizu, T.Shindo, and M.Tanaka

19. 19 In SPS2 (Focus point),   can be different from the SM prediction. Inconsistency between the Bd unitarity and  K. The squark mass splitting is larger for SPS 2.

20. 20 Summary If SUSY is a true symmetry, determining the SUSY breaking sector is one of the most fundamental issues. The SUSY breaking sector carries information on physics at a very high energy scale. We expect different patterns of deviations from SM predictions for different SUSY breaking scenarios and unification models. We studied the unitarity triangle and the b-s transition in rare B decays for four models: mSUGRA, two cases of SU(5) SUSY GUT with right-handed neutrinos, and MSSM with U(2) flavor symmetry. A large deviation is possible in the 1-2 transition for the degenerate case, and in the 2-3 transition for the non-degenerate case of SUSY GUT, and various signals appear for the case of U(2) favor symmetry. We also studied the parameter space based on Snowmass Points and Slopes (SPS). The deviation due to  K is sizable for SPS 2 (focus points) in the degenerate case of SUSY GUT. Super B factory is essential to discriminate various SUSY models.