1. Yasuhiro Okada (KEK) December 18, 2006 BNMII, Nara Women’s Univ.
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 deviation from the standard model in many observables.
Advantage of a planed super B factory is that there are several qualitatively different observables.
For new physics search, correlation 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 Diagonal tem: LHC/LC Off diagonal term:
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 how B physics is useful to explore the SUSY breaking sector, we take three models.
Minimal supergravity model
SU(5) SUSY GUT with right-handed neutrino
MSSM with U(2) flavor symmetry

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

7. SU(5) SUSY GUT with right-handed neutrino
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;….
Large flavor mixing in the neutrino sector can be a source of flavor mixing in the right-handed sdown sector.
Correlation with LFV processes (m -> eg, etc) is important.
New CP phases in the GUT embedding. (T.Moroi)

8. The LFV constraint depends on neutrino parameters
Neutrino mass
LFV mass terms for slepton (and sdown).
Two cases considered for MR.
Degenerate case
(MR )ij= M dij
Severe m->eg constraint
(2) Non-degenerate case
m ->eg suppressed
(Casas and Ibarra, Ellis-Hisano-Raidal-Shimizu)

9. MSSM with U(2) flavor symmetry
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; ….
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

10. Numerical results
We calculated SUSY effects to the following observables in the three models.
CP violation in K-K mixing (e).
Bd-Bd mixing, Bs-Bs mixing.
Mixing-induced CP violation in B ->J/yKs,
B->fKs, B->Ms g .
Direct CP violation in b->s g.

11. Unitarity triangle Small deviation in mSUGRA.
Bd unitarity triangle is closed,
but eK has a large SUSY
contribution in SU(5) GUT for
the degenerate MR case.
Bs mixing receives SUSY
effects for the non-degenerate
case.
Various SUSY contributions
for the U(2)flavor symmetry
model.
SU(5) GUT
Degenerate
Dm(Bs)/Dm(Bd)
SU(5) GUT
Non-degenerate
U(2) FS f3
A(B->J/yKs)

12. CP asymmetries in B ->f Ks and b-> sg
CP asymmetry
in B ->f Ks
CP asymmetry
in B -> K*g
Direct asymmetry
in b -> s g

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

14. Unitarity triangle The Bs mixing constraint is strong.
SU(5) GUT
Degenerate
The Bs mixing constraint is strong.
Survival points are reduced due to slight tension between |Vub| and f1 measurements
SU(5) GUT
Non-degenerate
U(2) FS

15. Difference between the Bd mixing angle and real 2f1
Need to determine |Vub| and f3 in a few % level to distinguish this
difference.

16. S(f Ks)-S(J/y Ks)
SU(5) GUT
Non-degenerate
SU(5) GUT
Degenerate
U(2) FS
Difference can be % for SU(5) GUT with non-degenerate case
and U(2) model.

17. Direct and mixing induce asymmetry in b to sg
Direct asymmetry in b -> s g
A few%
CP asymmetry in B -> K*g
10-20 %
SU(5) GUT
Degenerate
SU(5) GUT
Non-degenerate
U(2) FS

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

19. Tau and muon lepton flavor violation
LFV is a process that limit the parameter space.
SU(5) GUT
Degenerate
SU(5) GUT
Non-degenerate
U(2) FS
m->eg
m->eg and t->mg
t->mg

20. Electric dipole moments
Neutron and Hg electric dipole moment is another important limiting process.
Although theoretical uncertainty is still large, EDM is a promising signal for
models of 2-3 mixing of right-handed squark .
U(2) FS
SU(5) GUT
Non-degenerate
Estimation of neutron EDM from strange chromomagentic moment
in the chiral perturbation theory (J. Hsano and Y. Shimizu, 2004)

21. _ < a few % <~5% b->sg direct CP LFV EDM m->eg <O(10%)
Summary of possible deviation from the SM prediction
Bd- unitarity
Triangle test
T-dep CPV
in B->fKs, B->K*g
b->sg direct CP
in Bs->J/yf
LFV
EDM
mSUGRA _
SU(5)SUSY
GUT + nR
(degenerate)
m->eg
(non-degenerate)
<O(10%)
<~5%
t->mg
large
U(2) Flavor symmetry
< a few %

22. Summary
We have updated study of the flavor signals in three SUSY models.
The measurement of the Bs mixing already put strong constraints on possible deviations. Although the pattern of the deviation 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.