Flavored Electric Dipole Moments in Supersymmetric Standard Models

1
Flavored Electric Dipole Moments in
Supersymmetric Standard Models

• Minoru Nagai (KEK)

Ref Phys.Lett.B642,510 (2006) hep-ph/0606322
arXiv0712.1285 hep-ph
(arXiv080X.XXXX in preparation)
Collaborated with J. Hisano (ICRR), P.
Paradisi (Munich Tech. U.)
June 19, 2008
SUSY08 _at_ Seoul, Korea
2
Plan of my talk

• Introduction
• Flavored EDM at the LO (1-loop)
• Flavored EDM at the BLO
• Numerical Calculation in a SUSY GUT model
• Summary

3
Electric Dipole Moment
Electric Dipole Moment (EDM)
T P violating
In the field theory, where CPT symmetry is
conserved, the EDM for spin 1/2 fermion is given
by the following effective operator.
CP P violating
In the Standard Model (SM)
Only source of CP violation is the CP phase of
the CKM matrix.
Current bounds
( long range effect )
(no contribution up to 3 loop )
?
Sensitive to the Beyond SM physics
) We assume a PQ symmetry to suppress the
dangerous QCD term
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What can we probe by EDMs in supersymmetric SMs?

• Flavor-conserving terms
• complex in general
• These phases should be suppressed by some SUSY
  breaking mediation mechanisms.

strongly constrained by EDM experiments

• Flavor-violating terms
• complex hermit matrix
• off-diagonal components can have CP phases

Radiatively generated between the EW scale and
SUSY mediation scale
Flavored EDM
GUT structure Right-handed neutrino sector
FCNC, LFV
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2. Flavored EDM at the LO (1 loop)
CP violating Dim-5 operators
Quark EDM
Quark CEDM
Flavor-dependent 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 becomes
important in many models.
Case 1)
Case 2) Case 3)
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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
for
cf. Constraint from
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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
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3. Flavored EDM at the BLO
Importance of the BLO calculation

• Contributions from are generated only
  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 corrections are
generated?
Non-holomorphic Yukwa couplings
Diagonalization
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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)
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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
100
10 -25
(dRR) 31 (0.22)3
tanß 10
10
10 -26
1
MH 300 GeV
(dLL) 13 (0.22)3
10 -27
10 -1
200
1000
2000
500
1500
2000
3000
4000
5000
1000
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 mSUSYgt 1-2 TeV.

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Large tanß Corrections for EDMs
down quark EDM
31
2
Charged Higgs contribution
Chargino contribution
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4. Numerical Calculation in a SUSY GUT model
SU(5) GUT with Right-handed neutrinos
Matter multiplet
Superpotential
See-saw
for
Neutrino Yukawa couplings induce flavor-violating
soft masses both for quarks and leptons.
LFV?leptonic EDM
Left-handed slepton mixing
Neutrino Yukawa coupling
Right-handed sdown mixing
SFKs?hadronic EDM
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Down Quark EDM in SU(5) GUT with RNs (1)
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.
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Down quark EDM in SU(5) GUT with RNs (2)
down quark EDM
1000
900
800
Gluino
700
Charged Higgs
600
Chargino
500
400
300
200
100
100
1000
500
200
300
400
600
700
800
900

• For , contributions of chargino
  and charged Higgs is important.

• As the SUSY scale becomes large, charged Higgs
  mediated one becomes dominant due to the
  logarithm term (slow decoupling feature).

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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.
• It turns out that the charged-Higgs and chargino
  contributions become dominant in many parameter
  regions.
• We should include all of these contributions to
  discuss the prediction of EDMs in concrete
  models, such as SUSY GUTs.

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Back Up Slide
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Two-loop Chargino Contribution
Hisano, MN, Paradisi (2007)
Pure Higgsino contribution

• charge

• Light stop mass

• large top quark mass

Gluino contribution
Chargino contribution may also become dominant
over the gluino one.
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Constraints on neutrino sector by Hadronic EDMs
Hisano, Kakizaki, MN, Shimizu (2004)
CMSSM (only gluino contribution)
Down quark CEDM (e cm)
Strange quark CEDM (e cm)
Hg EDM
Neutron EDM
Right-handed tau neutrino mass (GeV)
Current experimental bound Future Neutron
Deuteron EDM dn10-28, dD10-(2930) (e cm)
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Observed EDMs and CP-odd Sources
Topic in this talk
Thallium EDM
Electron EDM
CP violating hadronic interactions
199Hg EDM
CP-odd Sources in New Physics
Quark CEDM
Deuteron EDM
Quark EDM
Neutron EDM
CP violating Dim-5 operator
quark CEDM
fermion EDM
Although there could be uncertainties in the
hadronic and atomic calculations, it can be
estimated as
Present experimental bounds
Future experiments aim to improve sensitivities
23 orders of magnitudes
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Sources of CP violation in SUSY SMs

• Flavor-conserving CP violating terms (SUSY CP
  Problem)

complex in
general O(1) CP phases of these parameters
induce too large EDMs. ex) Constrained MSSM
From neutron EDM experiments,
These phases might be suppressed by some SUSY
breaking mediation mechanisms. In other word,
the SUSY CP problem seems to require
other mechanisms to suppress EDMs such as A0,
heavy particles,
or
as a model set-up.