1. 1 Electroweak Baryogenesis and LC Yasuhiro Okada (KEK) 8 th ACFA LC workshop July 12, 2005, Daegu, Korea

2. 2 Baryon number of Universe Important interplay between cosmology and particle physics Three conditions to create baryon number of Universe Baryon number violation C and CP violation Departure from thermal equilibrium One clear reason for physics beyond the Standard Model.

3. 3 Two scenarios B+L violation is enhanced at high temperature in the Standard Model. (Weak sphaleron interaction) Successful Baryon Number Generation (1) B-L generation at temperature above the electroweak phase transition. (ex. Leptogenesis) (2) Baryon number generation at the electroweak phase transition =“Electroweak Baryogenesis”

4. 4 Contents Conditions for electroweak baryogenesis Examples in MSSM, etc. Electroweak baryogenesis and Higgs self- coupling measurement

5. 5 Strong first order phase transition. Expansion of a bubble wall. Various charge flows due to CP violation at the wall. Baryon number violation in the symmetric phase. Baryon number generation at EW phase transition Final baryon number depends on what charge asymmetry is generated, how charges are transported in the plasma, the wall velocity, etc.

6. 6 Condition of the strong first order transition The first order phase transition is needed for a bubble nucleation. The sphaleron transition rate should be suppressed in the broken phase at the critical temperature, in order not to erase the created baryon number. This condition is expressed as Strong first order phase transition.

7. 7 Finite temperature effective potential in the SM In the high temperature expansion (m/T <1) In order to satisfy  c/Tc>1, the Higgs mass should be less than 50 GeV, which is much smaller than LEP bound. More accurate calculation confirmed the same conclusion.

8. 8 Bosonic loop corrections Heavy Higgs boson loops in 2 Higgs doublet model Light stop loops in MSSM (Fermionic loops are not very effective) Modification of tree level potential Cubic terms in NMSSM and SUSY with extra U(1) SM with extra singlet. SM with dim 6 Higgs potential. etc. Possible way out New particles and/or modification of the Higgs sector is necessary. => Some form of collider signals.

9. 9 Electroweak Baryogenesis in MSSM Light right-handed stop (m(stop) < m(top)) is required for the strong 1 st order phase transition Sources of new CP violation Stop A term (At) chargino/neutralino mass matrixes (  parameter) Chargino effect turns out to be dominant source of the baryon number generation

10. 10 Required mass spectrum Right-handed stop (<top mass) LSP neutralino Chargino ( < ~ 200 GeV) Left-handed stop should be multi TeV ( precision EW and Higgs mass constraints) Numerical results on baryon number C.Balazs,M.Carena,A.Menon,D.E.Morrissey, C.E.M.Wagner 2005

11. 11 Phenomenological impacts Light right-handed stop whose mass is close to LSP neutralino. Light chargino/neutralino with a complex phase of sin  >0.1 => ILC physics EDM closed to the present bounds Parameter space allowed by EWBG and EDM C.Balazs,M.Carena,A.Menon,D.E.Morrissey, C.E.M.Wagner 2005

12. 12 Other examples SUSY U(1)’ model J.Kang, P.Langacker,T.Li, T.Liu,2005 1 st order phase transition from SHdHu SM with a low cut-off D.Bodeker,L.Fromme,S.J.Huber,M.Seniuch,2005 New CP violation from M (GeV)

13. 13 Higgs self-coupling constant and EWBG Electroweak baryogensis requires a large correction to the finite temperature effective potential. The zero temperature potential is also expected to receive a large correction. This will give a measurable impact to the triple Higgs boson coupling. We study this connection in 2HDM and MSSM. S.Kaenmura, Y. Okada, E.Senaha, 2004 Cf. An extension to quartic coupling, S.W. Ham and S.K.Oh, 2005 A similar connection in the model with a dim-6 Higgs potential term, C.Grojean,G.Servant, J.D.Wells, 2004

14. 14 Two Higgs doublet model Two cases Physical Higgs bosons: Higgs potential Heavy Higgs boson masses (1)Decupling case: (2) Non-decoupling case

15. 15 Effective potential in 2HDM Radiative correction to triple coupling constant (sin(  ) ~1) Correction to the cubic term in finite temp potential (high temp expansion, M=0)

16. 16 mh= 120 GeVmh= 160 GeV Numerical results on radiative correction to the triple coupling constant (not using high temp expansion) If we require the strong enough first order phase transition for EWBG, In MSSM case, ~6%

17. 17 Triple Higgs coupling measurement at ILC Expected efficiency is 40 %, S.Yamashita et.al, LCWS 04. Y. Yasui, et.al. GLC report R. Belusevic and G.Jikia 2004  HH

18. 18 Summary Electroweak baryogenesis offers an important connection between cosmology and particle physics. Successful baryon-number generation at the electroweak phase transition requires new physics related to the Higgs sector. Ex. Correction to the Higgs potential, new particles with a sizable interaction to the Higgs field New particles and new interactions relevant to the electroweak baryogensis should exist close to the Higgs mass scale. ILC will play an important role to test this scenario, by exploring new particles/interactions including possible new sources of CP violation.