Higgs-mediated chargino-neutralino two-loop EDMs Yingchuan Li University of Wisconsin YL, S. Profumo, M. Ramsey-Musolf, (arXiv:0806.2693) COSMO 2008, Madison

Outline WHY do we care about it? HOW is it done and WHAT is the result? Conclusion.

- Interplay between EW baryogenesis and EDMs Part I: Why are EDMs relevant? - Interplay between EW baryogenesis and EDMs

EDM - probe of CP violation CP violation: constraining theory SM: strong CP problem in SM; beyond SM: SUSY CP problem in MSSM; CP violation: needed in EW baryogenesis SM: not enough; beyond SM: marginally enough in MSSM; Non-observation of EDM versus EW baryogenesis?

Electroweak baryogenesis in MSSM resonant enhancement of CP violation: (Carena, et al. 1997,2001; Lee, et al. 2004) preferred ! chargino-neutralino scenario not preferred! stop scenario strong first-order phase transition: small stop masses: heavy left-handed and light right-handed stop; key wall parameter: small CP odd Higgs mass ; (Moreno, et al. 1998) 5

Chargino-neutralino scenario Crucial para. in chargino-neutralino scenario: CP violation source in chargino and neutralino sector: light RH stop mass: light CP odd Higgs mass: 6 6

Suppressed with heavy first two generation sfermions ! One-loop EDM in MSSM one-loop: CP violation source: both chargino-neutralino sector and sfermion sector mass parameters: Suppressed with heavy first two generation sfermions ! A.G.Cohen,D.B.Kaplan,A.E.Nelson,PLB,1996 a solution to SUSY CP problem; a way to reconcile with EW baryogenesis; 7

Sfermion two-loop EDM in MSSM 3rd generation sfermion two-loop: CP violation source: sfermion sector mass parameters: D. Chang, W.Y.Keung,A.Pilaftsis, PRL,1999; A.Pilaftsis, PLB,1999; D.Chang,W.F.Chang,W.Y.Keung,PLB,2000; 8

Most relevant part for EW baryogenesis! Chargino-neutralino two-loop EDM in MSSM chargino-neutralino two-loop: CP violation source: chargino-neutralino sector mass parameters: Most relevant part for EW baryogenesis! 9 9

Chargino-neutrlino two-loop EDM Part II: Chargino-neutrlino two-loop EDM

Chargino-neutralino 2-loop EDM -- diagrams Complete set of diagrams: Calculated: D.Chang,W.F.Chang,W.Y.Keung, PRD, 2002, 2005 A. Pilaftsis, Nucl. Phys.B,2002 G.Giudice,A.Romanino,PLB,2006 Uncalculated:

Chargino-neutralino 2-loop EDM – gauge choice Non-linear gauge: no couping. Diagram (c) vanishes. Non-linear Landau gauge: Diagram (d) vanishes. K. Fujikawa, PRD, 1973; J. Romao, A. Barroso, PRD, 1987 M. Gavela, G. Girardi, C. Malleville, P. Sorba, Nucl. Phys.B,1981

Chargino-neutralino 2-loop EDM – structure from upper loop ward-identity consistent structures. Strcutures for each contribution:

Chargino-neutralino 2-loop EDM – analytic result

Chargino-neutralino 2-loop EDM – numerical result ZA and WH are dominant contributions. Ref. point:

Conclusion Thank you !!! Chargino-neutralino 2-loop EDMs are the most relevant ones to EW baryogenesis. We calculate the new contributions from ZA and WH, which are dominant ones, making this set complete. The calculation is important for complete analysis of EDM and also its interplay with EW baryogenesis in MSSM. Thank you !!!