One-loop analysis of the 4-Femi contribution to the Atomic EDM within R-parity violating MSSM N. YAMANAKA (Osaka University) 2010/8/9 Sigma Hall Osaka Univ. In collaboration with T. 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 (d n ~ ~33 e cm, d e ~ e cm) (T-odd = CP-odd) (d n < 3.0 x e cm, d e < 1.6 x e cm, d Hg < 3.1 x e cm, … ) Inspection of EDM : → Good probe for large CP violation sources!

Object of study Investigate RPVMSSM contribution to the atomic EDM ( 199 Hg), at the one-loop level. Object: Update of 199 Hg 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

199 Hg EDM Diamagnetic atom !! W. C. Griffith et al., Phys. Rev. Lett. 102, (2009). d( 199 Hg) =(0.49 ± 1.29 ± 0.76) x 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 199 Hg EDM exp. (using C SP ). RPVMSSM

CP-odd electron-nucleon interaction ⇒ P-odd, CP-odd interaction, contribute to 199 Hg EDM !! Limits C SP < 5.2 x C PS < 5.1 x CTCT < 1.5 x e N ⇒ Dominant one-loop RPV contribution to C SP ⇒ Strongest constraints on C SP,C T, C PS from 199 Hg EDM : |d Hg | <3.1x e cm ( 199 Hg 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: fermionboson ⇒ 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 GeV (GUT) … + ~ log 

R-parity violation R-parity violation → lepton/baryon number violation R-parity : RPV lagrangian needed: ud eLeL ~ 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, (2000).  1j1 1j1 ’  jkk ’ 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 205 Tl EDM: Obtained limit via CP-odd e-N int. (C SP ) Constraint from 205 Tl EDM exp. data ( C SP < 3.4 x ) 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 1 st and 2 nd 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). | 121 | < 0.04 [e R ]CKM | 131 | < 0.05 [e R ]  decay ratio | ’ 221 |  | ’ 321 |  | ’ 231 | < 0.22 [d L ] -q inelastic scattering | ’ 331 | < 0.12 [d R ]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 integral CKM matrix RPV couplings RPV coupling ( ’) RPV coupling ( ) < 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(  1i1 ’ ia1 ): 7.3 x x (GeV) (i=2,3)

Comparison with other exp. data |  121 ’ 221 | < 4.8 x |  131 ’ 321 | < 6.0 x |  121 ’ 231 | < 8.8 x |  131 ’ 331 | < 6.0 x Limit from other exp. (current limit on RPV couplings): Limit from 199 Hg EDM (1-loop analysis): 7.3 x x ⇒ New constraints on CP phase of RPV couplings !! Limit from 199 Hg EDM (tree level, Herczeg 2000): | Im (  121 ’ 211 )| < 2.6 x | Im (  131 ’ 311 )| < 2.6 x | Im (  121 ’ 222 )| < 6 x | Im (  131 ’ 322 )| < 6 x | Im (  121 ’ 233 )| < 6 x | Im (  131 ’ 333 )| < 6 x (i=2,3) (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  121 ’ 221,  131 ’ 321,  121 ’ 231,  131 ’ 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) m  = 1321 MeV m  = 1116 MeV m  = 1189 MeV m u = 5.1 MeV m d = 9.3 MeV m s = 175 MeV How to build Nucleon level effective (scalar) interaction from quark level interaction qq L ~ L ~ NN q q q q q q