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

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

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

4. 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?

5. 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

6. 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

7. 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

8. 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

9. 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

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

11. 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:

12. 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

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

14. Chargino-neutralino 2-loop EDM – analytic result

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

16. 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 !!!