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One-loop analysis of the 4-Femi contribution to the Atomic EDM within R-parity violating MSSM

One-loop analysis of the 4-Femi contribution to the Atomic EDM within R-parity violating MSSM. N. YAMANAKA (Osaka University). In collaboration with T. Sato (Osaka U niv .), T. Kubota (Osaka U niv .). 2010 /8/9 Sigma Hall Osaka Univ. Contents. Introduction Atomic EDM

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One-loop analysis of the 4-Femi contribution to the Atomic EDM within R-parity violating MSSM

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  1. One-loop analysis of the 4-Femicontribution to the Atomic EDMwithin R-parity violating MSSM N. YAMANAKA (Osaka University) In collaboration with T. Sato (OsakaUniv.), T. Kubota (OsakaUniv.) 2010/8/9 Sigma Hall Osaka Univ.

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

  3. Introduction

  4. Go beyond the Standard Model Sakharov’s conditions: Conditions needed to realize matter Abundant Universe • Baryon/lepton number violating interactions • C &CP violation • Departure from thermal equilibrium Matter/photon ratio : CKM prediction too small!! ⇒ Need New physics with larger CP violation!! How to probe ? ⇒ Electric dipole moment!!

  5. Electric dipole moment (EDM) Properties: P, T-odd observable (T-odd = CP-odd) + - Very accurate measurement is possible (dn< 3.0 x 10-26e cm , de< 1.6 x 10-27e cm , dHg< 3.1 x 10-29e cm , … ) Small SM contribution (dn ~ 10-31~33e cm , de ~ 10-38e cm) Inspection of EDM : → Good probe for large CP violation sources!

  6. Object of study Atomic EDM is a very efficient probe to search for NP beyond SM. Study of Atomic EDM is now very active. Recently, Analysis of Atomic EDM (CP-odd e-N interaction) within RPVMSSM at the tree level (Herczeg, 2000) Update of 199Hg EDM experiment (Washington Univ., 2009) Object: Investigate RPVMSSM contribution to the atomic EDM (199Hg), at the one-loop level.

  7. Atomic EDM

  8. 199Hg EDM Diamagnetic atom !! Sensitivity to CP-odd mechanisms: Sensitive to nucleon EDMs , CP-odd electron-nucleon interactions , CP-odd nucleon-nucleon interaction, … Diamagnetic Atom EDM in SM is very small ⇒ Powerful probe of New physics ! Current exp. result: d(199Hg) =(0.49 ± 1.29 ± 0.76) x 10-29 e cm W. C. Griffith et al., Phys. Rev. Lett. 102, 101601 (2009).

  9. Outline of EDM calculation RPVMSSM M. Pospelov, A. Ritz., Ann. Phys. 318, 119 (2005). Our object: Obtain limit on RPV couplings from 199Hg EDM exp. (using CSP).

  10. CP-odd electron-nucleon interaction e ⇒ P-odd, CP-odd interaction, contribute to 199Hg EDM !! 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).

  11. SUSY and R-parity violation

  12. Supersymmetry (SUSY) ⇔ ⇒ Each particle has a “super-partner” fermion boson Symmetry between boson & fermion: Minimal Supersymmetric Standard Model (MSSM): ⇒ Gauge invariant, renormalizable log L + ~ ⇒ Phenomenological extension of the SM!! 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) …

  13. R-parity violation d u ~ eL 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 !! R-parity : R-parity violation → lepton/baryon number violation RPV lagrangian needed: ⇒ 45 interactions total Yukawa interaction!! Many RPV interactions are constrained phenomenologically (proton decay, double beta decay, etc)

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

  15. Previous work : Tree level (Herczeg, 2000) l*1j1 l1j1 Tree level analysis of RPVMSSM Obtained limit via CP-odd e-N int. (CSP) l’jkk l’*jkk Constraint from 205Tl EDM exp. data ( CSP< 3.4 x 10-7 ) d,s,b quark Limit obtained from 205Tl EDM: b quark contribution: s quark contribution: d quark contribution: ⇒ Is it possible to constrain other RPV couplings at the loop level? P. Herczeg, Phys. Rev. D61, 095010 (2000).

  16. 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. : | 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 M. Chemtob, Prog. Part. Nucl. Phys. 54, 71 (2005). […] denote SUSY particle mass in unit of 100 GeV

  17. Diagrams Enumerate all one-loop e-u&e-d interaction diagrams with 2 RPV couplings • ⇒ No contribution from Vertex loop diagram : • Renormalization of RPV couplings • No imaginary part • Other cancellation mechanism ⇒ Reduce to the analysis of box diagrams!

  18. 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

  19. One-loop RPV contribution to atomic EDM RPV coupling (l) (+ h.c.) RPV coupling (l’) CKM matrix Loop integral RPV couplings Scalar interaction < 5.2 x10-8

  20. Constraint to RPV couplings S-electron mass dependence of upper limit of Im( l*1i1l’ia1 ): (GeV) (GeV) Charm quark in the loop (a=2) Top quark in the loop (a=3) If s-electron mass 7.3 x 10-6 6.0 x 10-4 (i=2,3)

  21. Comparison with other exp. data 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 (SUSY mass = 100GeV) Limit from other exp. (current limit on RPV couplings): | 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 (SUSY mass = 100GeV) Limit from 199Hg EDM (1-loop analysis): 7.3 x 10-6 (i=2,3) 6.0 x 10-4 (SUSY mass = 100GeV) ⇒ New constraints on CP phase of RPV couplings !!

  22. Summary & future interest Summary: • 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 . Future interest: • Neutron EDM : one-loop analysis on quark-quark interaction

  23. Nucleon matrix element (quark -> nucleon) q q ~ nL ~ nL How to build Nucleon level effective (scalar) interaction from quark level interaction q q q N N q q q (Hisano-san’s talk) mX = 1321 MeV mL = 1116 MeV mS = 1189 MeV mu = 5.1 MeV md = 9.3 MeV ms = 175 MeV

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