Flavor induced EDMs Flavor induced EDMs with tanbeta enhanced with tanbeta enhanced

correctionscorrections

Flavor induced EDMs Flavor induced EDMs with tanbeta enhanced with tanbeta enhanced

correctionscorrectionsMinoru Nagai　

(ICRR, Univ. of Tokyo)

Aug. 4, 2007

Summer Institute 2007

In collaborated with: J.Hisano (ICRR), P.Paradisi (Valencia)

Phys.Lett.B642,510 (2006)

1. Introduction1. Introduction Supersymmetric standard models is the most well-

motivated model beyond the Standard Model.

Difficulty : SUSY CP & flavor problem

Blessings•Hierarchy problem•Gauge coupling unification

•Dark matter candidate•Light Higgs•・・・

CP phases and flavor structures must be highly constrained.

Off diagonal components of sfermion mass matrixes must be tiny.

Ex.) by Δm K

Hints for the SUSY

SMs

D term SUSY breaking terms

: complex hermit matrix

off-diagonal components can have CP phases Even if these is no phases at the tree level, it can be generated by radiative corrections.Null results of EDMs severely constrained these off diagonal element.

EDM measurements are sensitive to not only CP phases but also flavor structures.

What can we probe by EDMs in supersymmetric SMs?What can we probe by EDMs in supersymmetric SMs? F term SUSY breaking terms

: complex in general

These phases may be suppressed by some SUSY breaking & mediation mechanisms.

strongly constrained by EDM experiments

at 3 loop level

2. Flavor induced EDM 2. Flavor induced EDM CP violating Dim-5 operatorsQuark

EDMQuark CEDM

CP violating effects can be estimated by basis-independent measure of CP violation, Jarlskog invariants.

There is only one CP violating phase in the CKM matrix and the corresponding Jarlskog invariant is highly suppressed by the ninth orders of Yukawa couplings.

The Standard Model

Supersymmetric standard models

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)

The Standard Model

Jarlskog invariant

Case 1)Case 1)

gluino contribution to EDMs

[S.Dimopoulos & L.J.Hall (1995)]

An odd number of Yukawa coupling appear to have a chirality-flip

Heavy quark mass enhancement

Case 2)Case 2)

Case 3)Case 3)

Need couplings with both charged and neutral particles

There is no contribution at 1-loop

[M.Endo et al. (2004)]

Higgsino contribution to EDMs

3. New Higgs-mediated two loop contribution3. New Higgs-mediated two loop contribution

Charged Higgs contribution to EDMs

Effective Higgs coupling induced by radiative corrections to down-quark mass matrix

Non-decoupling at the large SUSY particle mass limit

Tree level 1-loop level

Features of the higgs-mediated two loop contributionFeatures of the higgs-mediated two loop contribution

down quark (C)EDM: dd/e (dcd) [cm]

200 1000 2000

Charged Higgs mass: MH+ [GeV]

10 -1

1

10

100

10 -26

10 -27

10 -25

500 1500 1000 2000 3000 4000 5000

Ratio of 1 and 2-loop contribution:

dd (Higgs) / dd (gluino)

SUSY particle mass: mSUSY [GeV]

tanβ= 10

MH+ = 300 GeV(δLL) 13 = (0.22)3

(δRR) 31 = (0.22)3

It is slowly decoupled for heavy charged Higgs mass.

It may dominate over 1-loop gluino contribution for mSUSY> 1-2 TeV.

Hadronic EDMs in SUSY GUT modelsHadronic EDMs in SUSY GUT models

We can investigate SUSY GUT models by considering the correlation between flavor physics in the quark sector and those in the lepton sector.

SUSY GUT models Unification of gauge couplings

+ Unification of (s)quarks and (s)leptons

SU(5) GUT with right-handed neutrinos Matter multiplet :

Left-handed slepton mixingRight-handed sdown mixing

LFV、 leptonic EDM

SΦKs 、 hadronic EDM

SUSY breaking mass terms of squarks and sleptons are correlated

Neutrino Yukawa coupling

Hadronic EDMs vs. LFV processesHadronic EDMs vs. LFV processes

Strange quark CEDM (cm)

SuperB

Deuteron

Deuteron

MEG

Down quark CEDM (cm) Here, we plot the gluino contribution and the total contri

bution (gluino + charged Higgs) for quark CEDMs changing MH+ between 200 GeV and 2000 GeV

Charged Higgs contributions modify quark (C)EDMs significantly

Non Universal Higgs mass scenario

Non-decoupling in the limit of Slow decoupling in by the logarithm term of the loop function The effective coupling are induced by tanbeta enhanced corrections

Why the Higgs-mediated contribution can become large?

Large tan β Corrections for EDMsLarge tan β Corrections for EDMs

How about other contributions?Systematic calculations are

needed!

Charged Higgs

Chargino

GluinoTotal

TotalGluino

Charged Higgs

CharginoGluino

(Leading)

We discussed the flavor induced EDMs with tanbeta enhanced corrections for Yukawa couplings.

4. Summary4. Summary

We found a charged-Higgs mediated 2-loop contribution to down quark (C)EDMs can become large and it already constrains some parameter spaces in SUSY SMs.

As long as the charged Higgs mass is light, this contribution is not decoupled even if SUSY particles is heavy and can become dominant for mSUSY> 1-2 TeV.

Even if charged Higgs is heavy, (C)EDMs originated from this contribution may be detected in future experiments due to the slow decoupling feature.

For very large tanbeta, various diagrams can become important. We calculated tanbeta enhanced corrections systematically and estimated these contributions.

Back Up SlideBack Up Slide

CP phase constraintsCP 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) ]

Hadronic EDMsHadronic EDMs

CP violating Dim-5 operatorquark EDM quark

CEDM Although there can be large hadronic uncertainty, it can be estimated as

[Hisano & Shimizu (2004) ]

Present experimental bounds

199Hg EDM

Neutron EDM

Deuteron EDM

ＣＰ violating hadronic interactions Quark

CEDM

Quark EDMQuark EDM

1. Write the SU(2)xU(1) invariant lagrangian and relate non-holomorphic Yukawa couplings to the corresponding quark mass corrections.

2. Diagonalize the quark masses and change to the CKM basis. Then relate the tree-level Yukawa couplings to the quark masses and the CKM matrix.

3. Putting them back to the original lagrangian then effective couplings are obtained.

Systematic calculation of tan beta enhanced correctionsSystematic calculation of tan beta enhanced corrections

Calculate as a function of loop factors and mixing parameters

Derive

Tree level Yukawa couplings are determined

can be expressed by and

Loop factors