1. Flavor Phenomenology in SUSY models
Yasuhiro Okada (KEK/Sokendai)
September 26, 2007
4th ICFP, KITPC, Beijing
with Toru Goto, Tetsuo Shindou, and Minoru Tanaka

2. Flavor physics in the LHC era
The LHC experiment will start to look at the TeV scale physics directly next year.
Past and ongoing experiments in flavor physics have already put strong constraints on new physics models. (KEK and SLAC B factories, Tevatron B physics, etc.)
Several new experiments are under construction, LHCb(B), BESIII(t,charm),MEG(m->eg), and future plans of Super B factory are considered at KEK and Frascati.

3. Energy frontier vs. flavor
0.001
0.01
0.1 1 10
Energy scale
Coupling strength
LHC
Tevatron
100 TeV
Upgraded
KEKB
If new particles are discovered at LHC, flavor physics can determine
couplings, mixings, and CP phases related to new phenomena, or
restrict possible scenarios.

4. Lepton flavor violation
SUSY and Favor
Slepton and squark mass matrixes are a window to SUSY breaking mechanisms and GUT scale interactions.
GUT Yukawa coupling
Neutrino Yukawa Coupling
Squark/slepton
mass matrixes
Origin of
SUSY breaking
SUSY spectrum
Quark favor signals
Lepton flavor violation
We can explore the fundamental structure of SUSY models
at high scales from quark and lepton flavor signals

5. LHC/ILC vs. Quark Flavor Signals/LFV
Squark/slepton mass matrix
Quark flavor changing
processes
LHC: Squark up to ~3 TeV.
Diagonal
Off-diagonal
Lepton flavor violation
LHC+ILC:
Squark/slepton mass
spectrum

6. B physics in three SUSY models
T.Goto, Y.O. Y.Shimizu, T.Shindou, and M.Tanaka, PRD(2002), (2004)
In order to illustrate how B physics is useful to distinguish different SUSY models, we calculated various quark flavor observables in three representative SUSY models.
Models
1. Minimal supergravity model (mSUGRA)
2. SU(5) SUSY GUT with right-handed neutrino
MSSM with U(2) flavor symmetry
Observables
Bd-Bd mixing, Bs-Bs mixing.
CP violation in K-K mixing (e).
Time-dependent CP violation in B ->J/yKs, B->fKs, B->K*g .
Direct CP violation in b->s g.

7. A new study on quark and lepton flavor signals in SUSY models
T.Goto, Y.O.T.Shindou, and M.Tanaka, 2007
We have extended our previous work in the light of new developments and prospects of future experimental programs.
1. Bs physics
We take the Bs mixing as a new constraint, and calculate time-dependent
CP asymmetry in Bs-> J/y f mode, which is expected to be measured
up to the precision of 0.01 at LHCb.
(CDF,2006)
2. Tau LFV
We have calculated t -> mg and t -> eg branching ratios in addition to m->eg
for models with right-handed neutrinos.
Current bounds are ~10-7 but 1-2 orders of improvements are possible at
a future Super B factory,
3. Several technical improvements for calculations are incorporated.

8. mSUGRA and neutrino and GUT Yukawa couplings
We consider:
mSUGRA model,
MSSM with the right-handed neutrinos,
SU(5) SUSY GUT with right-handed neutrinos.
Quark and neutrino Yukawa couplings are sources of squark and slepton flavor mixings.
Flavor univesrality of
SUSY breaking terms
at the cutoff scale
Quark FCNC
LFV
Quark Yukawa coupling
Neutrino Yukawa coupling Yq Yn
Neutrino seesaw model
mSUGRA
GUT
L.J.Hall,V.Kostelecky,S.Raby,1986;A.Masiero, F.Borzumati, 1986

9. Neutrino Yukawa coupling and LFV
LFV constraint depends on neutrino parameters
Neutrino mass
LFV mass terms for slepton (and sdown).
Three cases are considered for MR.
Degenerate case
(MR )ij= M dij
Severe m->eg constraint
Non-degenerate (I)
Non-degenerate (II)
m ->eg suppressed
(Casas and Ibarra, Ellis-Hisano-Raidal-Shimizu)

10. 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
We do not consider LFV processes in this model

11. Lepton flavor violation processes in SU(5) SUSY GUT with right-handed neutrinos
m->eg, t->mg,t->eg rates are calculated in three cases in the GUT model.
Degenerate
Non-degenerate (I)
Non-degenerate (II)
t->eg
t->mg
m->eg
slepton mass
3TeV

12. t->mg and m->eg can be close to the present bounds
We take MR= 4x1014 GeV, which corresponds to 0(1) neutrino Yukawa coupling constants.
Degenerate case:
B(m->eg) is the process that limits the SUSY parameter space, and can be close to the present bound even if the slepton mass is 3 TeV.
Non-degenerate (I)
t->mg and m->eg can be close to the present bounds
Non-degenerate (II)
t->eg and m->eg can be close to the present bounds.
m->eg vs. tLFV in non-degenerate (I)

13. b-s and b-d transition processes
We have calculated the following observables for mSUGRA, three cases of SUSY GUT with RHN, and the U(2) model.
S(K*g): Mixing-induced CP asymmetry of B->K*g
S(rg): Mixing-induced CP asymmetry of B->rg
A(sg): Direct CP asymmetry of b->sg
A(dg): Direct CP asymmetry of b->dg
DS(fKs)=S(fKs)-S(J/yKs):
Difference of mixing-induced asymmetries for B->fKs and B->J/yKs
S(Bs->J/yf): Mixing-induced asymmetry of Bs->J/yf
Chiral structure
New phase
Phase of the Bs mixing amplitude,
~-0.04 in the SM
New CP phase
We have taken account of constraints from LFV and EDM searches.

14. Mixing-induced CP asymmetry: S(B->K*g)
U(2) model
SUSY GUT non-deg (I)
mSUGRA
Super B
sdown mass
3 TeV
Deviation can be large in SUSY GUT non-deg(I) and U(2) case
Expected precision is at Super B factory.
Estimation of experimental reach from
Super KEKB LOI, SuperB:CDR, CERN WS on Flavour in the era of the LHC

15. Mixing-induced CP asymmetry: S(B->rg)
mSUGRA
SUSY GUT non-deg (II)
U(2) model
Super B
Expected precision is at Super B factory.

16. Direct CP Asymmety: A(b->sg)
mSUGRA
SUSY GUT non-deg (I)
U(2)
Super B
Some deviations from the SM in the U(2) case.
Precision will be at Super B factory.

17. DS(fKs)=S(B->fKs)-S(B->J/yKs)
mSUGRA
SUSY GUT non-deg (I)
U(2) model
Super B
Expected precision is at Super B factory.

18. S(Bs->J/yf) for a new CP phase in the Bs mixing amplitude
SUSY GUT non-deg (I)
U(2) model
mSUGRA
LHCb
Expected precision is 0.01 at LHCb
from talk by T.Nakata at “SUSY 2010’s”, Hokkaido Univ. June 2007.

19. Correlation between DmBs/DmBd and f3(g) of the Unitarity triangle
Present precision of f3
from tree processes
If the f3 angle is precisely determined by tree processes, we can extract new physics contributions in DmBs/DmBd with improved determination of the hadronic factor　(x2 =fBs2 BBs/fBd2 BBd) by lattice QCD.
Precision of f3 determination is 2.4 deg at
LHCb and 1-2 deg at Super B factory.

20. DmBs/DmBd vs. f3 U(2) model mSGURA SUSY GUT non-deg (II)
LHCb
Correlation in mSUGRA is the same as in the SM .
The error in the vertical axis is essentially the uncertainty of x.
This is a sensitive test for new physics contributions to Bs and Bd mixing
amplitudes unless they are cancelled as in the case of Minimal Flavor Violation.

21. Pattern of new physics signals
Promising signals
Possible deviations for some points
Pattern of deviations from the SM can provide a clue on physics determining
the structure of the SUSY breaking sector.

22. Conclusions
We have performed a comparative study on quark and lepton flavor signals for representative SUSY models; mSUGRA, MSSM with right-handed neutrinos, SU(5) SUSY GUT with right-handed neutrinos, and U(2) models.
Each model predicts a different pattern of the deviations from the SM in b-s and b-d quark transition processes and muon and tau LFV processes.
Bs physics at LHCb and tau LFV searches at a future B factory will be important parts of this program, along with the m->eg search at the MEG experiment.