One-loop analysis of the 4-Femicontribution to the Atomic EDMwithin R-parity violating MSSM

N. YAMANAKA(Osaka University)

2010/8/9Sigma HallOsaka Univ.

In collaboration withT. Sato (OsakaUniv.), T. Kubota (OsakaUniv.)

• Introduction• Atomic EDM• SUSY and R-parity violation• One-loop analysis of CP-odd e-N interaction• Summary

Contents

Introduction

Go beyond the Standard Model

Sakharov’s conditions:

• Baryon/lepton number violating interactions• C &CP violation• Departure from thermal equilibrium

Conditions needed to realize matter Abundant Universe

Matter/photon ratio : CKM prediction too small!!

⇒ Need New physics with larger CP violation!!

How to probe ?

⇒ Electric dipole moment!!

Electric dipole moment (EDM)

+

-

Properties:

P, T-odd observable

Very accurate measurement is possible

Small SM contribution (dn ~ 10-31~33e cm , de ~ 10-38e cm)

(T-odd = CP-odd)

(dn< 3.0 x 10-26e cm , de< 1.6 x 10-27e cm , dHg< 3.1 x 10-29e cm , … )

Inspection of EDM : → Good probe for large CP violation sources!

Object of study

Investigate RPVMSSM contribution to the atomic EDM (199Hg), at the one-loop level.

Object:

Update of 199Hg EDM experiment (Washington Univ., 2009)

Analysis of Atomic EDM (CP-odd e-N interaction) within RPVMSSM at the tree level (Herczeg, 2000)

Atomic EDM is a very efficient probe to search for NP beyond SM.Study of Atomic EDM is now very active.

Recently,

Atomic EDM

199Hg EDM

Diamagnetic atom !!

W. C. Griffith et al., Phys. Rev. Lett. 102, 101601 (2009).

d(199Hg) =(0.49 ± 1.29 ± 0.76) x 10-29 e cm

Current exp. result:

Diamagnetic Atom EDM in SM is very small

Sensitive to nucleon EDMs , CP-odd electron-nucleon interactions , CP-odd nucleon-nucleon interaction, …

Sensitivity to CP-odd mechanisms:

⇒ Powerful probe of New physics !

Outline of EDM calculation

M. Pospelov, A. Ritz., Ann. Phys. 318, 119 (2005).

Our object: Obtain limit on RPV couplings from 199Hg EDM exp. (using CSP).

RPVMSSM

CP-odd electron-nucleon interaction

⇒ P-odd, CP-odd interaction, contribute to 199Hg EDM !!

LimitsCSP < 5.2 x 10-8

CPS < 5.1 x 10-7

CT < 1.5 x 10-9

e

N

⇒ Dominant one-loop RPV contribution to CSP

⇒ Strongest constraints on CSP,CT, CPS from 199Hg EDM :

|dHg| <3.1x 10-29 e cm(199Hg EDM, Griffith et al., 2009)

J.S.M. Ginges, V.V. Flambaum, Phys. Rept. 397, 63 (2004).

SUSY and R-parity violation

Supersymmetry (SUSY)

Symmetry between boson & fermion:

fermion boson ⇒ Each particle has a “super-partner”⇔

⇒ Phenomenological extension of the SM!!

Minimal Supersymmetric Standard Model (MSSM):

⇒ Gauge invariant, renormalizable

Why SUSY?• SUSY cancels power divergences (Fine tuning)• SUSY can break the EW symmetry.• Dark matter candidates, new CP violation sources, etc.• Better coincidence of gauge couplings at 1016GeV (GUT)

…

+ ~ log L

R-parity violation

R-parity violation → lepton/baryon number violation

R-parity :

RPV lagrangian needed:

ud

eL~

Yukawa interaction!!Many RPV interactions are constrained phenomenologically(proton decay, double beta decay, etc)

Supersymmetric extension of the SM allows B or L interaction ⇒ We must impose R-parity conservation to forbid them

But this assumption is ad hoc !!

⇒ 45 interactions total

One-loop analysis of the CP-odd e-N interaction

Previous work : Tree level (Herczeg, 2000)

P. Herczeg, Phys. Rev. D61, 095010 (2000).

l*1j1 l1j1

l’*jkkl’jkk

⇒ Is it possible to constrain other RPV couplings at the loop level?

d quark contribution: s quark contribution: b quark contribution:

d,s,b quark

Limit obtained from 205Tl EDM:

Obtained limit via CP-odd e-N int. (CSP)

Constraint from 205Tl EDM exp. data( CSP< 3.4 x 10-7 )

Tree level analysis of RPVMSSM

Setup of Parameters

Setup of SUSY parameters:

• Soft breaking squark and slepton mass matrices are diagonal in flavor and L <-> R• Yukawa couplings of 1st and 2nd generation neglected• Massless neutrino• RPV sector does not contain any soft SUSY breaking terms• RPV sector does not contain Higgs-lepton mixing• SUSY particle mass = O(100 GeV)

Constrain on RPV couplings from other exp. :

M. Chemtob, Prog. Part. Nucl. Phys. 54, 71 (2005).

| l121 | < 0.04 [eR] CKM| l131 | < 0.05 [eR] t decay ratio| l’221 | < 1.2 x 10-2 [dR] K ->pnn| l’321 | < 1.2 x 10-2 [dR] K ->pnn| l’231 | < 0.22 [dL] n-q inelastic scattering| l’331 | < 0.12 [dR] B- decay

[…] denote SUSY particle mass in unit of 100 GeV

Diagrams

⇒ No contribution from Vertex loop diagram : • Renormalization of RPV couplings• No imaginary part• Other cancellation mechanism

⇒ Reduce to the analysis of box diagrams!

Enumerate all one-loop e-u&e-d interaction diagrams with 2 RPV couplings

Box diagrams

d-quark – electron interaction(exchange type)

u-quark – electron interaction

d-quark – electron interaction(direct type)2 diagrams can have significant contribution to the

atomic EDM with different coupling from the tree level

One-loop RPV contribution to atomic EDM

(+ h.c.)

Scalar interaction

Loop integralCKM matrix

RPV couplings

RPV coupling (l’)

RPV coupling (l)

< 5.2 x10-8

Constraint to RPV couplings

Charm quark in the loop (a=2) Top quark in the loop (a=3)

If s-electron mass

S-electron mass dependence of upper limit of Im( l*1i1l’ia1 ):

7.3 x 10-6

6.0 x 10-4

(GeV)(GeV)

(i=2,3)

Comparison with other exp. data

| l*121l’221 | < 4.8 x 10-4

| l*131l’321 | < 6.0 x 10-4

| l*121l’231 | < 8.8 x 10-3

| l*131l’331 | < 6.0 x 10-3

Limit from other exp. (current limit on RPV couplings):

Limit from 199Hg EDM (1-loop analysis):

7.3 x 10-6

6.0 x 10-4

⇒ New constraints on CP phase of RPV couplings !!

Limit from 199Hg EDM (tree level, Herczeg 2000):| Im ( l*

121l’211 )| < 2.6 x 10-9

| Im ( l*131l’311 )| < 2.6 x 10-9

| Im ( l*121l’222 )| < 6 x 10-9

| Im ( l*131l’322 )| < 6 x 10-9

| Im ( l*121l’233 )| < 6 x 10-7

| Im ( l*131l’333 )| < 6 x 10-7

(i=2,3)

(SUSY mass = 100GeV)

(SUSY mass = 100GeV)

(SUSY mass = 100GeV)

• We have analyzed the RPV scalar e-N interaction contribution to the atomic EDM at the one-loop level.

• The estimation yield 1~2 order tighter constraint on (CP phase of) RPV couplings l*

121l’221 , l*131l’321 , l*

121l’231 , l*131l’331 .

Summary & future interest

• Neutron EDM : one-loop analysis on quark-quark interaction

Future interest:

Summary:

Nucleon matrix element (quark -> nucleon)

(Hisano-san’s talk) mX = 1321 MeVmL = 1116 MeVmS = 1189 MeV

mu = 5.1 MeVmd = 9.3 MeVms = 175 MeV

How to build Nucleon level effective (scalar) interaction from quark level interaction

qq

nL~

nL~

N Nq

qq

q

qq