1. Minoru Nagai (ICRR, Univ. of Tokyo)
‘Flavored’ Electric Dipole Moments in Supersymmetric Theories 　
Minoru Nagai　
(ICRR, Univ. of Tokyo)
( KEK )
Ref: Phys.Lett.B642,510 (2006)
arXiv:  [hep-ph]
Collaborated with:
J.Hisano (ICRR), P.Paradisi (Munich, Tech. U.)
Feb. 22, 2008
特定領域「フレーバー物理の新展開」研究会

2. Sensitive to the Beyond SM physics
1. Introduction
Electric Dipole Moment (EDM)
The EDM for spin 1/2 fermion is given by the following effective operator.
CP & P violating
Hadronic EDMs (dn, dHg) are generated by the CP violating operators, such as quark EDMs and CEDMs (ChromoElectric Dipole Moments).
Quark EDM
Quark CEDM
Current experimental bound ……
Future :
The Standard Model (SM)
Only source of CP violation is the CP phase of the CKM matrix.
（　　　　　　　） ⇒
Sensitive to the Beyond SM physics

3. Many sources of CP violation
The Minimal Supersymmetric Standard Model (MSSM)
Many sources of CP violation
Phases of gaugino masses, A term and B term.
Phases of off diagonal components in the sfermion mass matrices
strongly constrained by EDM experiments
They might be suppressed by some SUSY breaking & mediation mechanisms
: complex hermit matrix
Off-diagonal components can have CP phases.
Null results of EDMs severely constrained these off diagonal element.
We systematically discussed the flavor induced EDMs originated from the squark flavor mixing. Especially we included tanbeta enhanced threshold corrections, which appear to be very important to discuss them.

4. 2. Flavored EDM at the LO (1-loop)
CP violating Dim-5 operators
Quark EDM
Quark CEDM
CP violating effects can be estimated by basis-independent measure of CP violation, Jarlskog invariants. SM
There is only one CP violating phase in the CKM matrix.
at 3 loop level
MSSM
There are Jarlskog invariants originated from new CP phases of squark mass matrix. In this talk, we consider the down quark (C)EDM, which tend to dominate the up quark one.
Case 1) Case 2) Case 3)

5. gluino contribution to EDMs
Case 1)
[S.Dimopoulos & L.J.Hall (1995)]
Jarlskog invariant
An odd number of Yukawa coupling appear to have a chirality-flip
gluino contribution to EDMs
Heavy quark mass enhancement
cf. Constraint from :

6. There is no contribution at 1-loop
Case 2)
[M.Endo et al. (2004)]
Higgsino contribution to EDMs
Case 3)
Need couplings with both charged and neutral particles
There is no contribution at 1-loop

7. 4. Flavored EDM at the BLO Importance of the BLO calculation
Contributions from are generated only at above two-loop levels.
At the BLO, tanbeta enhanced interactions are generated through the radiative corrections to the quark mass terms. They give corrections to the EDMs at least.
How such tanbeta enhanced interactions are generated?
Non-holomorphic Yukwa couplings
Diagonalization

8. Higgs-mediated Two-loop Contribution
Effective Higgs coupling induced by radiative corrections to down-quark mass matrix
Down quark mass :
Tree level
1-loop level
Non-decoupling at the large SUSY particle mass limit
Charged Higgs contribution to EDMs
[Hisano, MN, Paradisi (2006)]

9. Features of the Higgs-mediated Two-loop Contribution
Ratio of 1 and 2-loop contribution:
dd (Higgs) / dd (gluino)
down quark (C)EDM: dd/e (dcd) [cm]
10 -25
100
(δRR) 31 = (0.22)3
tanβ= 10 10
10 -26 1
MH+ = 300 GeV
(δLL) 13 = (0.22)3
10 -27
10 -1
200
500
1000
1500
2000
1000
2000
3000
4000
5000
Charged Higgs mass: MH+ [GeV]
SUSY particle mass: mSUSY [GeV]
It is slowly decoupled for heavy charged Higgs mass.
It may dominate over 1-loop gluino contribution for mSUSY> 1-2 TeV.

10. Tanβ Enhanced Corrections for EDMs
down quark EDM
Charged Higgs
Chargino
Gluino
Total
Gluino (1-loop) 2 31
Charged Higgs contribution
Chargino contribution

11. Prediction in SU(5) SUSY GUT with RNs
down quark EDM
-26 10
Chargino
-27 10
Gluino
Charged Higgs
-28 10
Total
-29 10 5 10 60
In the concrete SUSY GUT models, not only gluino but also chargino and charged-Higgs may contribute to the EDMs at the same order of magnitude.

12. 4. Summary
We discussed the flavored EDMs, which are sensitive to the non-minimal flavor structure of squark masses and already constrain some parameter spaces in the MSSM.
Especially we classified the relevant CP-odd phases in terms of Jarlskog invariants, and performed systematical calculation at the BLO.
Tanbeta enhanced corrections play important role to discuss the prediction of EDMs in the MSSM.
In the case of and/or , charged-Higgs contributions tend to become important. Chargino contributions also become dominant for large tanbeta.
We should include all of these contributions to discuss the prediction of EDMs in concrete models, such as SUSY GUTs.

13. Back Up Slide

14. CP phase constraints
From the neutron EDM experiment, CP phases in the MSSM are constrained by
Here, we use the following formula.
[M.Pospelov and A.Ritz (1999) ]

15. Present experimental bounds
Hadronic EDMs
199Hg EDM
Neutron EDM
Deuteron EDM
ＣＰ violating hadronic interactions
Quark CEDM
Quark EDM
CP violating Dim-5 operator
quark EDM
quark CEDM
Although there can be large hadronic uncertainty, it can be estimated as
[Hisano & Shimizu (2004) ]
Present experimental bounds