1. 岡田 安弘 （ＫＥＫ、総合研究大学院大学） ２００８年６月２５日 日本大学
フレーバーで探る超対称模型
岡田　安弘　（ＫＥＫ、総合研究大学院大学）
２００８年６月２５日　日本大学

2. Flavor in the LHC era
LHC will give a first look at the TeV scale physics.
　The mass of the Higgs boson alone is an important hint for possible new physics scenarios.
Flavor structure of the TeV scale physics is largely unknown.
　 Patterns of the deviations from the SM predictions are a key to distinguish new physics models.
New flavor experiments are coming. LHCb, B physics at ATLAS and CMS, MEG, Super B, etc.

3. EDM ~0 SUSY CP Lepton flavor Quark flavor Neutrino mixing B,D,K LFV~0
SM has a characteristic feature among various flavor and CP signals.
EDM ~0
SUSY CP
Lepton flavor
Neutrino mixing
LFV~0
Quark flavor
B,D,K
slepton mixing
GUT
Relationship may be quite different for new physics contributions.

4. Content of this talk
Quark and lepton flavor physics processes sensitive to the TeV scale physics.
Study of quark and lepton flavor signals in various cases of SUSY models.
　　　　　　　　　　　T.Goto,Y.O., T.Shindou,M.Tanaka, arXiv:

5. Two B factrories
Two B factory experiments, Belle at KEKB and BABAR at PEPII have been very successful.
total
KEKB
PEPII
Over 1ab-1 (=1000 fb-1) in total corresponding to 109 B-Bbar pairs.

6. Status of quark flavor physics
The Cabibbo-Kobayashi-Maskawa matrix works perfectly.

7. Series of discoveries 2001 CPV in B->J/y Ks 2001 b->sll
2004 Direct CPV in B->Kp
2006 b->dg
2006 B->tn
2006 Bs –Bs mixing at Tevatron
D-D mixing
All are more or less consistent with the CKM prediction.

8. Is this enough?
Not, to study New Physics effects.
In order to disentangle new physics
effects, we should first determine CKM
parameters by “tree-level” processes.
Fit from tree level processes
|Vub|, f3/g
Bd mixing and CP asymmetries
eK and B(K->pnn)
Bs mixing and CP asymmetries +
We know (or constrain) which sector is affected by new physics.
Improvement of f3/g is essential.

9. Super B factory
Physics case of future B factory experiments has been studied in many places.
Super KEKB LoI (hep-ex/ )
SLAC Super B workshop (hep-ph/ )
Super B CDR (arXiv: )
CERN workshop “Flavour in the era of the LHC”
At KEK, we started study on future upgrade of　the current B factory experiment in 2001 by theorists, experimentalists and accelerator physicists. The effort is still continuing . Super KEKB aims to increase the luminosity by a factor of 50.
The goal of a super B factory is to explore physics at the TeV scale from B, D, and t decays.

10. Basic of B factory physics: Time-dependent CP asymmetry in B decays
Carter-Sanda, Bigi-Sanda　1981
Time –dependent asymmetry can arise from the interference of two paths
in the B-> f decay amplitude.
A_f : Direct CP asymmnetry
S_f: Mixing –induced (Time-dependent) CP asymmetry

11. In the Standard Model, the B- B bar mixing amplitude have the phase 2f1W
In general, the decay amplitude depends on several weak phases
( hf : CP eigenvalue of f)
If f is an CP eigen state, and the decay amplitude is dominated by
one weak phase amplitude, then

12. Physics sensitivity at a Super B factory.
Super KEKB LoI
(1) Unitarity triangle
50 ab -1
5 ab -1
Consistency test at % level is possible at 50 ab -1.

13. (2) CP asymmetry in penguin-dominated processes
Current data
Time-dependent CP asymmetry
(Dominant decay diagrams)
B->J/yKs
“tree”
B->fKs
“penguin”
New phase (ex SUSY)
“sin 2f1“ is the same in the SM

14. (3) Rare B decays
There are many rare decay processes sensitive to new physics effects.
Electroweak penguin processes offer several theoretical clean observables.
Inclusive and exclusive b->sg
Inclusive and exclusive b->dg
Inclusive and exclusive b->sll
1. Direct CP violation in b->sg,dg
(New phase)
2. Mixing-induced CP asymmetry in B->K*g, Ksp0g.
(Right-handed photon operator)
3. Lepton forward-backward asymmetry
in b ->sll.

15. Expected precisions at Super B factory
Super KEKB study and SuperB CDR study; ab-1
Current results
0.39 ± 0.17
b-s
transition
0.61 ± 0.07
0.58 ± 0.20
Charged
Higgs
error ~ EW
penguin
−0.09 ± 0.24
0(10%) physics (Now)
=> 0(1%) physics (Future)
CERN Flavour WS report: arXiv:    

16. CPV in Bs system at LHCb
Measurement of CP violation in the Bs system is a major goal of the LHCb experiment.
Many are parallel to the Bd system.
S(Bd->J/y Ks)
S(Bd->fKs)
S(Bd->K*g)
Time dep. CP in Bs->J/yf
“Bs mixing phase”
Time-dep. CPV in Bs-> ff
“b-s penguin phase”
Time-dep. CPV in Bs->fg
“right-handed current”
2fb-1 (1year)
M.Merk,a talk at CERM TH Institute, May 26,2008

17. m and t Lepton Flavor Violation
B( t->mg)
Sensitive to slepton flavor mixings
The MEG experiment will search for B(m->eg) up to The current upper bound is 1.2 x
One to two orders improvements are expected at a Super B factory for tau LFV searches.
S.Banerjee, TAU 06
Super B factory, ab-1
arXiv:    

18. SUSY and flavor physics
LHC experiments will be a crucial test for existence of SUSY. (Squark/gluino mass reach 2-3 TeV, A light Higgs boson)
The role of flavor physics is to determine the flavor structure of squark/slepton mass matrixes. (new sources of flavor mixing and CP phases)
Squark/slepton 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

19. Different assumptions on the SUSY breaking sector
Minimal Flavor Violation (ex. mSUGRA)
SUSY GUT with see-saw neutrinos
SUSY breaking
Flavor symmetry
Effective SUSY
etc.
How to distinguish these models from factory observables?

20. Quark and lepton flavor physics in various SUSY models
T.Goto, Y.O. Y.Shimizu, T.Shindou, and M.Tanaka,2002, 2004
T.Goto,Y.O., T.Shindou,M.Tanaka, arXiv:
In order to illustrate how future flavor experiments are useful to distinguish different SUSY models, we calculated various quark and lepton flavor observables in representative SUSY models.
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 ,B->rg.
Direct CP violation in b->s g,b->dg
m->eg, t->mg, t->eg
Models
1. Minimal supergravity model (mSUGRA)
2. SUSY seesaw model
2. SU(5) SUSY GUT with right-handed neutrino
MSSM with U(2) flavor symmetry
(CDF,2006)

21. mSUGRSA with GUT/Seesaw Yukawa interaction
Yukawa interactions at the GUT scales induce quark and lepton flavor signals.
In the SU(5) setup, the right-handed sdown sector can receive flavor mixing
due to the neutrino Yukawa couplings.
Neutrino Yukawa coupling
Quark Yukawa coupling
Interactions
at GUT/seesaw scale
Quark flavor signals
Time-dep CP asymmetries in
B->fKs
B -> K*g
Bs->J/yf
Lepton flavor violation in
m->eg
t->mg
t->eg
L.J.Hall,V.Kostelecky,S.Raby,1986;A.Masiero, F.Borzumati, 1986, R.Barbieri,L.Hall,1994,
R.Barbieri,L.Hall.A.Strumia, 1995, S.Baek,T.Goto,Y.O, K.Okumura, 2001;T.Moroi,2000;
A.Masiero, M.Piai,A Romanino, L.Silvestrini,2001 D.Chang, A.Masiero, H.Murayama,2003
J.Hisano,and Y.Shimizu, 2003, M.Ciuchini, et.al, 2004, 2007…

22. 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)

23. 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

24. 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

25. We take MR= 4x1014 GeV, which corresponds to 0(1) neutrino Yukawa coupling constants.
m->eg, t->mg,t->eg rates are large depending on the texture of the neutrino Yukawa coupling constants
In the 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.
Due to the GUT interaction, the m->eg is a promising signal along with tau LFV in the non-degenerate cases.

26. Correlaton between m->eg and t->mg/t->eg
Non-degenerate (I)
Non-degenerate (II)
MEG: B(m->eg) – 10-14
Super B: B (t->mg, t->eg) O(10-9)

27. 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.
Direct and mixing-induced CP asymmetry of b->sg
Direct and mixing-induced CP asymmetry of b->dg
Difference of CP asymmetries for B->fKs and B->J/yKs
Mixing-induced asymmetry of Bs->J/yf
Phase of the Bs mixing amplitude,
~-0.04 in the SM
Precisely determined at the LHCb experiment.
We have taken account of constraints from LFV and EDM searches.

28. 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.

29. 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.

30. 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.

31. 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.

32. 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.

33. b-s and b-d transitions
Summary table of flavor signals for mSUGRA, SUSY seesaw, SUSY GUT,
MSSA with U(2) flavor symmetry
LFV
b-s and b-d transitions
Pattern of deviation from the SM predictions are different for various cases considered.

34. 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.
These signals can provide important clues on physics at very high energy scales if SUSY particles are found at LHC.