Higgs physics as a probe of electroweak baryogenesis

Transcription

1 Higgs physics as a probe of electroweak baryogenesis Eibun Senaha IPMU, May 27, 205.

2 Outline Introduction! Review of electroweak baryogenesis (EWBG)! Real singlet-extended SM (rsm)! Electroweak phase transition (EWPT) & sphaleron decoupling condition! Impact on the hhh coupling! Summary

3 Higgs and cosmology Higgs boson was discovered. ATLAS+CMS combined Higgs mass [PRL4,9803 (205)] m H = ± 0.24 GeV = ± 0.2(stat.) ± 0.(syst.) GeV What is the implications of Higgs physics for cosmology? - cosmic baryon asymmetry EW baryogenesis - dark matter inert Higgs, Higgs portal etc. - inflation Higgs inflation - etc We discuss EW baryogenesis in light of recent LHC data.

4 Higgs and cosmology Higgs boson was discovered. ATLAS+CMS combined Higgs mass [PRL4,9803 (205)] m H = ± 0.24 GeV = ± 0.2(stat.) ± 0.(syst.) GeV What is the implications of Higgs physics for cosmology? - cosmic baryon asymmetry EW baryogenesis - dark matter inert Higgs, Higgs portal etc. - inflation Higgs inflation - etc We discuss EW baryogenesis in light of recent LHC data.

5 Baryon Asymmetry of the Universe (BAU) Our Universe is baryon-asymmetric. CMB = n B n =(6.047 ± 0.074) 0 0, BBN = n B n =( ) 0 0 (95% CL). [PDG204] Sakharov criteria ( 67) BAU must arise () Baryon number (B) violation (2) C and CP violation (3) Out of equilibrium - After inflation - Before Big-Bang Nucleosynthesis (T O() MeV).

6 Many possibilities [Shaposhnikov, J.Phys.Conf.Ser.7:02005,2009.]. GUT baryogenesis. 2. GUT baryogenesis after preheating. 3. Baryogenesis from primordial black holes. 4. String scale baryogenesis. 5. Affleck-Dine (AD) baryogenesis. 6. Hybridized AD baryogenesis. 7. No-scale AD baryogenesis. 8. Single field baryogenesis. 9. Electroweak (EW) baryogenesis. 0. Local EW baryogenesis.. Non-local EW baryogenesis. 2. EW baryogenesis at preheating. 3. SUSY EW baryogenesis. 4. String mediated EW baryogenesis. 5. Baryogenesis via leptogenesis. 6. Inflationary baryogenesis. 7. Resonant leptogenesis. 8. Spontaneous baryogenesis. 9. Coherent baryogenesis. 20. Gravitational baryogenesis. 2. Defect mediated baryogenesis. 22. Baryogenesis from long cosmic strings. 23. Baryogenesis from short cosmic strings. 24. Baryogenesis from collapsing loops. 25. Baryogenesis through collapse of vortons. 26. Baryogenesis through axion domain walls. 27. Baryogenesis through QCD domain walls. 28. Baryogenesis through unstable domain walls. 29. Baryogenesis from classical force. 30. Baryogenesis from electrogenesis. 3. B-ball baryogenesis. 32. Baryogenesis from CPT breaking. 33. Baryogenesis through quantum gravity. 34. Baryogenesis via neutrino oscillations. 35. Monopole baryogenesis. 36. Axino induced baryogenesis. 37. Gravitino induced baryogenesis. 38. Radion induced baryogenesis. 39. Baryogenesis in large extra dimensions. 40. Baryogenesis by brane collision. 4. Baryogenesis via density fluctuations. 42. Baryogenesis from hadronic jets. 43. Thermal leptogenesis. 44. Nonthermal leptogenesis.

7 Many possibilities [Shaposhnikov, J.Phys.Conf.Ser.7:02005,2009.]. GUT baryogenesis. 2. GUT baryogenesis after preheating. 3. Baryogenesis from primordial black holes. 4. String scale baryogenesis. 5. Affleck-Dine (AD) baryogenesis. 6. Hybridized AD baryogenesis. 7. No-scale AD baryogenesis. 8. Single field baryogenesis. 9. Electroweak (EW) baryogenesis. 0. Local EW baryogenesis.. Non-local EW baryogenesis. 2. EW baryogenesis at preheating. 3. SUSY EW baryogenesis. 4. String mediated EW baryogenesis. 5. Baryogenesis via leptogenesis. 6. Inflationary baryogenesis. 7. Resonant leptogenesis. 8. Spontaneous baryogenesis. 9. Coherent baryogenesis. 20. Gravitational baryogenesis. 2. Defect mediated baryogenesis. 22. Baryogenesis from long cosmic strings. 23. Baryogenesis from short cosmic strings. 24. Baryogenesis from collapsing loops. 25. Baryogenesis through collapse of vortons. 26. Baryogenesis through axion domain walls. 27. Baryogenesis through QCD domain walls. 28. Baryogenesis through unstable domain walls. 29. Baryogenesis from classical force. 30. Baryogenesis from electrogenesis. 3. B-ball baryogenesis. 32. Baryogenesis from CPT breaking. 33. Baryogenesis through quantum gravity. 34. Baryogenesis via neutrino oscillations. 35. Monopole baryogenesis. 36. Axino induced baryogenesis. 37. Gravitino induced baryogenesis. 38. Radion induced baryogenesis. 39. Baryogenesis in large extra dimensions. 40. Baryogenesis by brane collision. 4. Baryogenesis via density fluctuations. 42. Baryogenesis from hadronic jets. 43. Thermal leptogenesis. 44. Nonthermal leptogenesis.

8 Many possibilities [Shaposhnikov, J.Phys.Conf.Ser.7:02005,2009.]. GUT baryogenesis. 2. GUT baryogenesis after preheating. 3. Baryogenesis from primordial black holes. 4. String scale baryogenesis. 5. Affleck-Dine (AD) baryogenesis. 6. Hybridized AD baryogenesis. 7. No-scale AD baryogenesis. 8. Single field baryogenesis. 9. Electroweak (EW) baryogenesis. 0. Local EW baryogenesis.. Non-local EW baryogenesis. 2. EW baryogenesis at preheating. 3. SUSY EW baryogenesis. 4. String mediated EW baryogenesis. 5. Baryogenesis via leptogenesis. 6. Inflationary baryogenesis. 7. Resonant leptogenesis. 8. Spontaneous baryogenesis. 9. Coherent baryogenesis. 20. Gravitational baryogenesis. 2. Defect mediated baryogenesis. 22. Baryogenesis from long cosmic strings. 23. Baryogenesis from short cosmic strings. 24. Baryogenesis from collapsing loops. 25. Baryogenesis through collapse of vortons. 26. Baryogenesis through axion domain walls. 27. Baryogenesis through QCD domain walls. 28. Baryogenesis through unstable domain walls. 29. Baryogenesis from classical force. 30. Baryogenesis from electrogenesis. 3. B-ball baryogenesis. 32. Baryogenesis from CPT breaking. 33. Baryogenesis through quantum gravity. 34. Baryogenesis via neutrino oscillations. 35. Monopole baryogenesis. 36. Axino induced baryogenesis. 37. Gravitino induced baryogenesis. 38. Radion induced baryogenesis. 39. Baryogenesis in large extra dimensions. 40. Baryogenesis by brane collision. 4. Baryogenesis via density fluctuations. 42. Baryogenesis from hadronic jets. 43. Thermal leptogenesis. 44. Nonthermal leptogenesis. Electroweak baryogenesis (EWBG) Higgs physics. st scenario that we can verify or falsify with experimental data.

9 Electroweak baryogenesis B violation: anomalous process! [Kuzmin, Rubakov, Shaposhnikov, PLB55,36 ( 85) ] Sakharov s criteria C violation: chiral gauge interaction! 0 $ X i=,2,3 (3q i L + l i L) (LH fermions) CP violation: CKM matrix and other complex phases in the beyond the SM! Out of equilibrium: st -order EW phase transition (EWPT) with expanding bubble walls +,--%."/0'()*+% average bubble radius O(0 6 )m [Carrington, Kapusta, PRD47, ( 93) 5304]!"#$%&'()*+% " BAU can arise by the growing bubbles.

10 EW Baryogenesis mechanism symmetric phase H: Hubble constant broken phase f, f $ f, f CP

11 EW Baryogenesis mechanism symmetric phase H: Hubble constant broken phase () f, f $ f, f CP () Asymmetries arise ( CPV) but no BAU. n B = n L b n L b =0 + n R b n R b =0 =0

12 EW Baryogenesis mechanism symmetric phase H: Hubble constant broken phase () (2) f, f $ f, f CP () Asymmetries arise ( CPV) but no BAU. n B = n L b n L b (2) LH part changes ( sphaleron) -> BAU n B = n L b n L b + n R b n R b =0 =0 =0 changed + n R b n R b n B =0

13 EW Baryogenesis mechanism symmetric phase H: Hubble constant broken phase (3) () (2) f, f $ f, f CP () Asymmetries arise ( CPV) but no BAU. n B = n L b n L b (2) LH part changes ( sphaleron) -> BAU n B = n L b n L b + n R b n R b =0 =0 =0 + n R b n R b n B =0 (3) If (b) B <H the BAU can survive. changed

14 EW Baryogenesis mechanism symmetric phase How do we test this scenario? H: Hubble constant broken phase (3) () (2) f, f $ f, f CP () Asymmetries arise ( CPV) but no BAU. n B = n L b n L b (2) LH part changes ( sphaleron) -> BAU n B = n L b n L b + n R b n R b =0 =0 =0 + n R b n R b n B =0 (3) If (b) B <H the BAU can survive. changed

15 EW Baryogenesis mechanism symmetric phase H: Hubble constant How do we test this scenario? -> cannot redo EWPT in lab. exp. So, test Sakharov criteria instead. broken phase (3) () (2) f, f $ f, f CP () Asymmetries arise ( CPV) but no BAU. n B = n L b n L b (2) LH part changes ( sphaleron) -> BAU n B = n L b n L b + n R b n R b =0 =0 =0 + n R b n R b n B =0 (3) If (b) B <H the BAU can survive. changed

16 EW Baryogenesis mechanism symmetric phase H: Hubble constant How do we test this scenario? -> cannot redo EWPT in lab. exp. So, test Sakharov criteria instead. broken phase (3) () (2) f, f $ f, f CP probe by collider physics Higgs physics etc () Asymmetries arise ( CPV) but no BAU. n B = n L b n L b (2) LH part changes ( sphaleron) -> BAU n B = n L b n L b + n R b n R b =0 =0 =0 + n R b n R b n B =0 (3) If (b) B <H the BAU can survive. changed

17 EW Baryogenesis mechanism symmetric phase H: Hubble constant How do we test this scenario? -> cannot redo EWPT in lab. exp. So, test Sakharov criteria instead. broken phase (3) () (2) f, f $ f, f CP probe by CPV physics EDMs, B decays etc probe by collider physics Higgs physics etc () Asymmetries arise ( CPV) but no BAU. n B = n L b n L b (2) LH part changes ( sphaleron) -> BAU n B = n L b n L b + n R b n R b =0 =0 =0 + n R b n R b n B =0 (3) If (b) B <H the BAU can survive. changed

18 EW Baryogenesis mechanism symmetric phase H: Hubble constant How do we test this scenario? -> cannot redo EWPT in lab. exp. So, test Sakharov criteria instead. broken phase (3) () (2) f, f $ f, f CP probe by CPV physics EDMs, B decays etc Relevant particles are light (<TeV) probe by collider physics Higgs physics etc () Asymmetries arise ( CPV) but no BAU. n B = n L b n L b (2) LH part changes ( sphaleron) -> BAU n B = n L b n L b + n R b n R b =0 =0 =0 + n R b n R b n B =0 (3) If (b) B <H the BAU can survive. changed

19 (b) B <H B-changing rate in the broken phase is (b) B (T ) (prefactor)e E sph/t Esph Energy sphaleron instanton E sph is proportional to the Higgs VEV - 0 Ncs E sph / v(t ) Veff what we need is large Higgs VEV after the EWPT EWPT has to be strong st order!! (b) B (T C) <H(T C ) v C T C & 0 v C T>Tc T=Tc T<Tc (GeV)

20 (b) B <H B-changing rate in the broken phase is (b) B (T ) (prefactor)e E sph/t E sph Esph Energy sphaleron instanton E sph is proportional to the Higgs VEV - 0 B = 3 N CS Ncs E sph / v(t ) Veff what we need is large Higgs VEV after the EWPT EWPT has to be strong st order!! (b) B (T C) <H(T C ) v C T C & 0 v C T>Tc T=Tc T<Tc (GeV)

21 How do we get st -order EWPT? st(2nd) order PT = discontinuities in st(2nd) derivatives of free energy 2 nd order PT st order PT

22 How do we get st -order EWPT? st(2nd) order PT = discontinuities in st(2nd) derivatives of free energy 2 nd order PT st order PT st -order PT Negative contributions in V eff.

23 How do we get st -order EWPT? st(2nd) order PT = discontinuities in st(2nd) derivatives of free energy 2 nd order PT st order PT st -order PT Negative contributions in V eff. From where?

24 Origins of the negative contributions in V eff. 2 representative cases.

25 Origins of the negative contributions in V eff. 2 representative cases.. Thermal loop driven case e.g. SM, MSSM. doublet Higgs thermal boson loop V (boson) ('; T ) 3 T (m2 (')) 3/2 2 Tg 3 ' 3 = m 2 =g 2 ' 2 2

26 Origins of the negative contributions in V eff. 2 representative cases.. Thermal loop driven case e.g. SM, MSSM. doublet Higgs thermal boson loop V (boson) ('; T ) 3 T (m2 (')) 3/2 2 Tg 3 ' 3 = m 2 =g 2 ' 2 2 [N.B.] If m 2 (') =g 2 ' 2 + M 2 ' M 2,no ' 3 term!!

27 Origins of the negative contributions in V eff. 2 representative cases.. Thermal loop driven case e.g. SM, MSSM. doublet Higgs thermal boson loop V (boson) ('; T ) 3 T (m2 (')) 3/2 2 Tg 3 ' 3 = m 2 =g 2 ' 2 2 Typical signals Deviations of hgg and/or hγγ and/or hhh couplings [N.B.] If m 2 (') =g 2 ' 2 + M 2 ' M 2,no ' 3 term!!

28 Origins of the negative contributions in V eff. 2 representative cases.. Thermal loop driven case e.g. SM, MSSM. doublet Higgs thermal boson loop V (boson) ('; T ) 3 T (m2 (')) 3/2 2 Tg 3 ' 3 = m 2 =g 2 ' 2 2 Typical signals Deviations of hgg and/or hγγ and/or hhh couplings [N.B.] If m 2 (') =g 2 ' 2 + M 2 ' M 2,no ' 3 term!! 2. Tree driven case e.g. rsm, NMSSM. singlet Higgs V 0 3 µ HS ' 2 H' S + µ S ' 3 S 3 M(µ HS,µ S )(' 2 H + ' 2 S) 3/2

29 Origins of the negative contributions in V eff. 2 representative cases.. Thermal loop driven case e.g. SM, MSSM. doublet Higgs thermal boson loop V (boson) ('; T ) 3 T (m2 (')) 3/2 2 Tg 3 ' 3 = m 2 =g 2 ' 2 2 Typical signals Deviations of hgg and/or hγγ and/or hhh couplings [N.B.] If m 2 (') =g 2 ' 2 + M 2 ' M 2,no ' 3 term!! 2. Tree driven case e.g. rsm, NMSSM. singlet Higgs V 0 3 µ HS ' 2 H' S + µ S ' 3 S 3 M(µ HS,µ S )(' 2 H + ' 2 S) 3/2 can be negative!

30 Origins of the negative contributions in V eff. 2 representative cases.. Thermal loop driven case e.g. SM, MSSM. doublet Higgs thermal boson loop V (boson) ('; T ) 3 T (m2 (')) 3/2 2 Tg 3 ' 3 = m 2 =g 2 ' 2 2 Typical signals Deviations of hgg and/or hγγ and/or hhh couplings [N.B.] If m 2 (') =g 2 ' 2 + M 2 ' M 2,no ' 3 term!! 2. Tree driven case e.g. rsm, NMSSM. singlet Higgs V 0 3 µ HS ' 2 H' S + µ S ' 3 S 3 M(µ HS,µ S )(' 2 H + ' 2 S) 3/2 can be negative! Typical signals Deviations of HVV and/or Hff and/or hhh couplings.

31 Current status of EWBG

32 Current status of EWBG - SM EWBG was excluded. No st -order PT for m h =25 GeV. [Kajantie at al, PRL77,2887 ( 96); Rummukainen et al, NPB532,283 ( 98); Csikor et al, PRL82, 2 ( 99); Aoki et al, PRD60,0300 ( 99). Laine et al, NPB73,80( 99)]

33 Current status of EWBG - SM EWBG was excluded. No st -order PT for m h =25 GeV. v C T C & not satisfied [Kajantie at al, PRL77,2887 ( 96); Rummukainen et al, NPB532,283 ( 98); Csikor et al, PRL82, 2 ( 99); Aoki et al, PRD60,0300 ( 99). Laine et al, NPB73,80( 99)]

34 Current status of EWBG - SM EWBG was excluded. No st -order PT for m h =25 GeV. v C T C & not satisfied [Kajantie at al, PRL77,2887 ( 96); Rummukainen et al, NPB532,283 ( 98); Csikor et al, PRL82, 2 ( 99); Aoki et al, PRD60,0300 ( 99). Laine et al, NPB73,80( 99)] - MSSM EWBG was excluded. light stop scenario is inconsistent with LHC data [D. Curtin, P. Jaiswall, P. Meade., JHEP08(202)005; T. Cohen, D. E. Morrissey, A. Pierce, PRD86, (202); K. Krizka, A. Kumar, D. E. Morrissey, PRD87, (203)]

35 Current status of EWBG - SM EWBG was excluded. No st -order PT for m h =25 GeV. v C T C & not satisfied [Kajantie at al, PRL77,2887 ( 96); Rummukainen et al, NPB532,283 ( 98); Csikor et al, PRL82, 2 ( 99); Aoki et al, PRD60,0300 ( 99). Laine et al, NPB73,80( 99)] - MSSM EWBG was excluded. light stop scenario is inconsistent with LHC data v C T C & not satisfied [D. Curtin, P. Jaiswall, P. Meade., JHEP08(202)005; T. Cohen, D. E. Morrissey, A. Pierce, PRD86, (202); K. Krizka, A. Kumar, D. E. Morrissey, PRD87, (203)]

36 Current status of EWBG - SM EWBG was excluded. No st -order PT for m h =25 GeV. v C T C & not satisfied [Kajantie at al, PRL77,2887 ( 96); Rummukainen et al, NPB532,283 ( 98); Csikor et al, PRL82, 2 ( 99); Aoki et al, PRD60,0300 ( 99). Laine et al, NPB73,80( 99)] - MSSM EWBG was excluded. light stop scenario is inconsistent with LHC data v C T C & not satisfied [D. Curtin, P. Jaiswall, P. Meade., JHEP08(202)005; T. Cohen, D. E. Morrissey, A. Pierce, PRD86, (202); K. Krizka, A. Kumar, D. E. Morrissey, PRD87, (203)] - Not enough data to exclude other models (2HDM, NMSSM etc). Anyway, collider test of EWBG will be done based on the sphaleron decoupling condition, v C & T C

37 What s next? - No benchmark scenario. - Colored particles (squarks) may not play a role in realizing strong st -order PT. (due to severe LHC bounds) - EWPT may be simply described by extended Higgs sector. SM + SU(2) n-tuplet Higgs, n=,2,3, [N.B.] CP violation comes from (chargino, neutralino)-sector which would not be relevant in studying EWPT. (bosons are more important than fermions) We will consider a simple case, SM+SU(2) singlet Higgs.

38 Electroweak phase transition in the real singlet-extended SM (rsm) in collaboration with Kaori Fuyuto (Nagoya U) Ref. Phys.Rev.D90, 0505 (204), [arxiv: ]

39 Toward Higgs precision (Higgcision) - Higgs sector will be clarified with better accuracy at the coming LHC and ILC. [arxiv: , M. Peskin] - Theoretical uncertainties in the EWBG calculation also have to be minimized. In the literature, v C T C > is usually used. But, r.h.s depends on Higgs mass In this talk, we evaluate this condition more precisely, and study its impact on Higgs phenomenology. SM case sph =.6 (m h = 25 GeV)

40 Toward Higgs precision (Higgcision) - Higgs sector will be clarified with better accuracy at the coming LHC and ILC. [arxiv: , M. Peskin] - Theoretical uncertainties in the EWBG calculation also have to be minimized. But, r.h.s depends on Higgs mass In this talk, we evaluate this condition more precisely, and study its impact on Higgs phenomenology. SM case sph =.6 (m h = 25 GeV)

41 Toward Higgs precision (Higgcision) - Higgs sector will be clarified with better accuracy at the coming LHC and ILC. [arxiv: , M. Peskin] - Theoretical uncertainties in the EWBG calculation also have to be minimized. v C T C > sph must be used. But, r.h.s depends on Higgs mass In this talk, we evaluate this condition more precisely, and study its impact on Higgs phenomenology. SM case sph =.6 (m h = 25 GeV)

42 Real singlet-extended SM (rsm) Particle content: SM + S: (,,0) - simple extension of the SM - MSSM extended models have singlet Higgs (e.g., NMSSM) Higgs potential: V 0 = µ 2 HH H + H (H H) 2 + µ HS H HS + HS 2 H HS 2 + µ 3 SS + m2 S 2 S2 + µ0 S 3 S3 + S 4 S4, Scalar fields: H(x) = p 2 G + (x) v + h(x)+ig 0 (x), S(x) =v S + s(x).

43 Real singlet-extended SM (rsm) Particle content: SM + S: (,,0) - simple extension of the SM - MSSM extended models have singlet Higgs (e.g., NMSSM) Higgs potential: V 0 = µ 2 HH H + H (H H) 2 + µ HS H HS + HS 2 H HS 2 + µ 3 SS + m2 S 2 S2 + µ0 S 3 S3 + S 4 S4, Scalar fields: H(x) = p 2 G + (x) v + h(x)+ig 0 (x), S(x) =v S + s(x). H-S mixings are important to have strong st -order PT.

44 Minimization = v apple µ 2 H + H v 2 + µ HS v S + HS 2 v2 S =0, = v S apple µ 3 S v S + m 2 S + µ 0 Sv S + S v 2 S + µ HS 2 v 2 v S + HS 2 v2 =0, Mass matrix: M 2 H = 2 h s M 2 H h s 2 H v 2 µ HS v + HS vv S µ µ HS v + HS vv 3 S S v S + µ 0 S v S +2 S vs 2 µ HS 2 v 2 v S!, which can be diagonalized by h s = cos sin sin cos H H 2 2 [ /4, /4]

45 Minimization = v apple µ 2 H + H v 2 + µ HS v S + HS 2 v2 S =0, = v S apple µ 3 S v S + m 2 S + µ 0 Sv S + S v 2 S + µ HS 2 v 2 v S + HS 2 v2 =0, Mass matrix: M 2 H = 2 h s M 2 H h s 2 H v 2 µ HS v + HS vv S µ µ HS v + HS vv 3 S S v S + µ 0 S v S +2 S vs 2 µ HS 2 v 2 v S!, which can be diagonalized by h s = cos sin 25 GeV Higgs sin H cos H 2 2 [ /4, /4]

46 Vacuum structure - Shape of the T=0 Higgs potential in an example. - Vacuum structure is complex. EW vac. is not always global.

47 Vacuum structure EW vacuum - Shape of the T=0 Higgs potential in an example. - Vacuum structure is complex. EW vac. is not always global.

48 Vacuum structure EW vacuum - Shape of the T=0 Higgs potential in an example. - Vacuum structure is complex. EW vac. is not always global.

49 Vacuum structure ' S various vacua: [Funakubo, Tao, Toyoda, PTP4, ( 05) 369] EW : v 6= 0, v S 6=0, I:v =0, v S 6=0, II : v 6= 0, v S =0, SYM : v = v S =0 I SYM EW (v, v S ) II ' Global min. condition: V (EW) (v, v S ) <V(', ' S ) For example, V 0 = V (I) 0 (0, v S) V (EW) 0 (v, v S ) = H 4 v4 + µ HS 4 v2 v S + HS 4 v2 v 2 S + µ3 S 2 ( v S v S ) V 0 has to be positive. µ 0 S v S = 2 S 6 ( v3 S v 3 S) apple µ 0 S ± S 4 ( v4 S v 4 S). q µ 02 S 4 S m 2 S However, V 0 < 0 would occur if v S gets large. (small S) [NOTE]: Relatively large v S is needed for type-b EWPT (see later)

50 Higgs couplings Higgs-gauge bosons L HVV = v (cos H sin H 2 ) 2m 2 W W + µ W µ + m 2 ZZ µ Z µ, Higgs-fermions L Yukawa = X f m f v (cos H sin H 2 ) ff. Normalized couplings: apple V = g H VV g SM hv V = cos, apple F = g H ff g SM hff = cos. We collectively denote apple apple V = apple F

51 Higgs couplings Higgs-gauge bosons L HVV = v (cos H sin H 2 ) 2m 2 W W + µ W µ + m 2 ZZ µ Z µ, Higgs-fermions L Yukawa = X f m f v (cos H sin H 2 ) ff. Normalized couplings: apple V = g H VV g SM hv V = cos, apple F = g H ff g SM hff = cos. We collectively denote apple apple V = apple F

52 Higgs couplings Higgs-gauge bosons L HVV = v (cos H sin H 2 ) 2m 2 W W + µ W µ + m 2 ZZ µ Z µ, Higgs-fermions L Yukawa = X f m f v (cos H sin H 2 ) ff. Normalized couplings: apple V = g H VV g SM hv V = cos, apple F = g H ff g SM hff = cos. We collectively denote apple apple V = apple F

53 LHC constraints κ f Constraints from 25 GeV Higgs CMS Observed 68% CL 95% CL 99.7% CL SM Higgs fb (8 TeV) + 5. fb (7 TeV) κ V - Direct/Indirect searches put some constraints on the 2nd Higgs mass and coupling. 2 C' sin Direct search of 2nd Higgs - - CMS up to 5. fb (7 TeV) + up to 9.7 fb (8 TeV) Obs., Obs., Obs., Β new Β new Β new = 0.0 = 0.2 = 0.5 Γ = Γ SM (Β new = 0.5) µ h(25) Exp., Β new = 0.0 Exp., Β new = 0.2 Exp., Β new = 0.5 =.00 ± m H [GeV] Signal strength of the 2nd Higgs µ 0 = C 02 ( B new )

54 LHC constraints κ f Constraints from 25 GeV Higgs CMS Observed 68% CL 95% CL 99.7% CL SM Higgs fb (8 TeV) + 5. fb (7 TeV) prediction of rsm κ V - Direct/Indirect searches put some constraints on the 2nd Higgs mass and coupling. 2 C' sin Direct search of 2nd Higgs - - CMS up to 5. fb (7 TeV) + up to 9.7 fb (8 TeV) Obs., Obs., Obs., Β new Β new Β new = 0.0 = 0.2 = 0.5 Γ = Γ SM (Β new = 0.5) µ h(25) Exp., Β new = 0.0 Exp., Β new = 0.2 Exp., Β new = 0.5 =.00 ± m H [GeV] Signal strength of the 2nd Higgs µ 0 = C 02 ( B new )

55 Effective potential To discuss EWPT, we use the effective potential. V e (' H, ' S,T)=V 0 (' H, ' S )+V (' H, ' S )+V (' H, ' S,T)+V daisy (' H, ' S,T). where V (' H, ' S )= X i V (' H, ' S,T)= X i with V daisy (' H, ' S,T)= n i m 4 i (' H, ' S ) 64 2 n i T I B,F I B,F (a 2 )= X j n j T 2 h Z 0 ln m2 i (' H, ' S ) µ 2 c i m 2 i (' H, ' S ), n H = n H2 = n G 0 =, n G ± =2, n W =2 3, n Z =3, n t = n b = 4N c, T 2 dx x 2 ln e p x 2 +a 2, M 2 j (' H, ' S,T) 3/2 m 2 j(' H, ' S ) 3/2i,,

56 Patterns of EWPT Diverse patterns of the phase transitions. [K.Funakubo, S. Tao, F. Toyoda., PTP4,369 (2005)] B A: SYM I EW B: SYM I EW C: SYM II EW D: SYM EW I A D EW C SYM II Type B Before EW symmetry breaking, singlet develops a VEV. Difference between type A and type B: barrier exists in type B, no barrier in type A

57 Type-B PT ' S ' = z cos, ' S = z sin + v S EW : (v, v S ) I 0 :(0, v S ) I 0 z EW ' V (z, ; T )=c 0 + c z + c 2 z 2 c 3 z 3 + c 4 z 4! T =TC c 4 z 2 (z z C ) 2. v C T C = z C T C c = Ec 4 s c h(µ HS + HS v S )c 2 /2+(µ 0 S /3+ S v S )s 2 i /T C ( H c 4 + HS s 2 c 2 + S s 4 )/2 To get the strong st -order PT, numerator and/or denominator Size of v S is constrained by the vacuum stability EWPT is reduced to the SM-like as! 0( v S! v S ). type B > type A

58 Type-B PT ' S ' = z cos, ' S = z sin + v S EW : (v, v S ) I 0 :(0, v S ) I 0 z EW ' V (z, ; T )=c 0 + c z + c 2 z 2 c 3 z 3 + c 4 z 4! T =TC c 4 z 2 (z z C ) 2. v C T C = z C T C c = Ec 4 s c h(µ HS + HS v S )c 2 /2+(µ 0 S /3+ S v S )s 2 i /T C ( H c 4 + HS s 2 c 2 + S s 4 )/2 To get the strong st -order PT, numerator and/or denominator Size of v S is constrained by the vacuum stability EWPT is reduced to the SM-like as! 0( v S! v S ). type B > type A

59 Type-B PT ' S ' = z cos, ' S = z sin + v S EW : (v, v S ) I 0 :(0, v S ) I 0 z EW ' V (z, ; T )=c 0 + c z + c 2 z 2 c 3 z 3 + c 4 z 4! T =TC c 4 z 2 (z z C ) 2. v C T C = z C T C c = Ec 4 s c h(µ HS + HS v S )c 2 /2+(µ 0 S /3+ S v S )s 2 i /T C ( H c 4 + HS s 2 c 2 + S s 4 )/2 To get the strong st -order PT, numerator and/or denominator Size of v S is constrained by the vacuum stability EWPT is reduced to the SM-like as! 0( v S! v S ). type B > type A

60 Type-B PT ' S ' = z cos, ' S = z sin + v S EW : (v, v S ) I 0 :(0, v S ) I 0 z EW ' V (z, ; T )=c 0 + c z + c 2 z 2 c 3 z 3 + c 4 z 4! T =TC c 4 z 2 (z z C ) 2. v C T C = z C T C c = thermal loop origin Ec 4 s c To get the strong st -order PT, h(µ HS + HS v S )c 2 /2+(µ 0 S /3+ S v S )s 2 i /T C ( H c 4 + HS s 2 c 2 + S s 4 )/2 numerator and/or denominator Size of v S is constrained by the vacuum stability EWPT is reduced to the SM-like as! 0( v S! v S ). type B > type A

61 Type-B PT ' S ' = z cos, ' S = z sin + v S EW : (v, v S ) I 0 :(0, v S ) I 0 z EW ' V (z, ; T )=c 0 + c z + c 2 z 2 c 3 z 3 + c 4 z 4! T =TC c 4 z 2 (z z C ) 2. v C T C = z C T C c = thermal loop origin Ec 4 s c To get the strong st -order PT, tree origin h(µ HS + HS v S )c 2 /2+(µ 0 S /3+ S v S )s 2 i /T C ( H c 4 + HS s 2 c 2 + S s 4 )/2 numerator and/or denominator Size of v S is constrained by the vacuum stability EWPT is reduced to the SM-like as! 0( v S! v S ). type B > type A

62 Strong st order PT m H2 = 70 GeV, v S = 90 GeV, µ 0 S = 30 GeV, µ HS = 80 GeV apple ' 0.9 is mixing angle between H and S. larger gives strong st -order PT. (v C /T C > for > 3 deg.)

63 Strong st order PT m H2 = 70 GeV, v S = 90 GeV, µ 0 S = 30 GeV, µ HS = 80 GeV v S (T C ) apple ' 0.9 is mixing angle between H and S. larger gives strong st -order PT. (v C /T C > for > 3 deg.)

64 Strong st order PT m H2 = 70 GeV, v S = 90 GeV, µ 0 S = 30 GeV, µ HS = 80 GeV v S (T C ) apple ' 0.9 EW vacuum is metastable is mixing angle between H and S. larger gives strong st -order PT. (v C /T C > for > 3 deg.)

65 Sphaleron decoupling condition After the EWPT, the sphaleron process has to be decoupled. (b) B (T ) (prefactor)e E sph/t <H(T ).66 g T 2 /m P g massless dof, (SM) m P Planck mass.22x0 9 GeV E sph =4 ve/g 2 (g 2 : SU(2) gauge coupling), v(t ) T > g apple ln N 2ln 4 E(T ) T 00 GeV + sph (T ), - Sphaleron energy gives the dominant effect. - We evaluate E(Tc), (Tc).

66 Sphaleron decoupling condition After the EWPT, the sphaleron process has to be decoupled. (b) B (T ) (prefactor)e E sph/t <H(T ).66 g T 2 /m P g massless dof, (SM) m P Planck mass.22x0 9 GeV E sph =4 ve/g 2 (g 2 : SU(2) gauge coupling), v(t ) T > g apple ln N 2ln 4 E(T ) T 00 GeV + sph (T ), - Sphaleron energy gives the dominant effect. - We evaluate E(Tc), (Tc).

67 Sphaleron decoupling condition m H2 = 70 GeV, v S = 90 GeV, µ 0 S = 30 GeV, µ HS = 80 GeV conventional criterion apple '

68 Sphaleron decoupling condition m H2 = 70 GeV, v S = 90 GeV, µ 0 S = 30 GeV, µ HS = 80 GeV conventional criterion apple ' (T C )= (.2-.3)

69 Sphaleron decoupling condition m H2 = 70 GeV, v S = 90 GeV, µ 0 S = 30 GeV, µ HS = 80 GeV conventional criterion (T C )= (.2-.3)

70 Sphaleron decoupling condition m H2 = 70 GeV, v S = 90 GeV, µ 0 S = 30 GeV, µ HS = 80 GeV conventional criterion (T C )= (.2-.3)

71 Sphaleron decoupling condition m H2 = 70 GeV, v S = 90 GeV, µ 0 S = 30 GeV, µ HS = 80 GeV conventional criterion (T C )= (.2-.3)

72 Sphaleron decoupling condition m H2 = 70 GeV, v S = 90 GeV, µ 0 S = 30 GeV, µ HS = 80 GeV conventional criterion (T C )= (.2-.3) - v C /T C > (T C ) is satisfied for > 5 deg.

73 hhh coupling - We may see a remnant of st-order EWPT by measuring Higgs self-coupling. Veff! T>Tc! 0 T=Tc T<Tc (GeV)! v C /T C -> hhh e.g., 2HDM [Kanemura, Okada, E.S., PLB606,(2005)36] (T C ) determines the minimum deviation of hhh.

74 hhh coupling hhh coupling in the SM. SM H H H = 3m2 H v m2 H 32 2 v 2 + X i=w,z,t,b n i m 4 i 2 2 m 2 H v The dominant one-loop correction comes from top loop hhh coupling in the rsm. rsm,tree H H H =6 apple rsm H H H = rsm,tree H H H + rsm,loop H H H, Hvc 3 + µ HS 2 s c 2 + HS 2 s c (vs + v S c )+ µ 0 S 3 + Sv S s 3, rsm,loop H H H = c 3 3 H + c S + c s 3 2 S + s 3 3 S, Larger gives the larger deviation from the SM value. (To have strong st order PT, ( HS,µ HS ) have to be large.)

75 H H H contours in (m H2, apple) plane % 30% % 0.85 v C /T C > (T C ) % EW vacuum is not global [GeV] H H H ' 6% for apple ' 0.97 and 60 GeV. m H2. 69 GeV, H H H ' 27% for apple ' 0.95, and 63 GeV. m H2. 76 GeV.

76 H H H contours in (m H2, apple) plane % 30% % 0.85 v C /T C > (T C ) % EW vacuum is not global [GeV] H H H ' 6% for apple ' 0.97 and 60 GeV. m H2. 69 GeV, H H H ' 27% for apple ' 0.95, and 63 GeV. m H2. 76 GeV.

77 H H H contours in (m H2, apple) plane % 30% % 0.85 v C /T C > (T C ) % EW vacuum is not global If v C T C > [GeV] H H H ' 6% for apple ' 0.97 and 60 GeV. m H2. 69 GeV, H H H ' 27% for apple ' 0.95, and 63 GeV. m H2. 76 GeV.

78 H H H contours in (m H2, apple) plane % 30% % 0.85 v C /T C > (T C ) % EW vacuum is not global [GeV] If 72 v C T C > H H H ' 6% for apple ' 0.97 and 60 GeV. m H2. 69 GeV, H H H ' 27% for apple ' 0.95, and 63 GeV. m H2. 76 GeV.

79 H H H contours in (m H2, apple) plane % 30% % 0.85 v C /T C > (T C ) % EW vacuum is not global [GeV] If 72 v C T C > 82 H H H ' 6% for apple ' 0.97 and 60 GeV. m H2. 69 GeV, H H H ' 27% for apple ' 0.95, and 63 GeV. m H2. 76 GeV.

80 [arxiv: , M. Peskin] Higgs coupling LHC/ILC can probe EWBG-favored region.

81 e events surviving the event selection before the mass criteria and angular cuts a malized to the number hhh of expected coupling events after at the full LHC event selection. The ttx c s t t( lepton) and t tγ, while Others includes c cγγ, b bγ j, b bjjand jjγγ. Projected limit on the total HH yield (events) s ATL-PHYS-PUB ATLAS Simulation Preliminary - = 4 TeV: 3000 fb Exp. 95% CLs ± σ ± 2 σ λ / λ SM 8: 95% CLs limit (dashed line) on the size of[ilc an additional white paper, HH contribution ] summ hhh/ hhh = 3%

82 Summary In the light of LHC data, MSSM EWBG was excluded. Other models are still viable. As a simple example, we have discussed the EW phase transition and sphaleron decoupling condition in SM+S. v C /T C > (.-.2) in the typical cases. We also studied the deviation of the hhh coupling from the SM value based on the improved sphaleron decoupling condition. The deviation is greater than that based on the conventional criterion v C /T C >. -> hhh

83 Backup

84 apple vs. H H H 50 SM H HH HHH SM H HH HHH = rsm Smaller gives larger HHH.

85 apple vs. H H H 50 SM H HH HHH SM H HH HHH = rsm (v C /T C =.2 > (T C )=.9) Smaller gives larger HHH.

86 apple vs. H H H SM H HH HHH SM H HH HHH = rsm (v C /T C =4.59 > (T C )=.9) (v C /T C =.2 > (T C )=.9) Smaller gives larger HHH.

87 Benchmark points Z2-symmetric S S2 S3 S4 H-S mixing parameters λ HS λ HS,µ HS λ HS,µ HS µ HS PT type D B B B m H2 [GeV] α [degrees] v S [GeV] µ HS [GeV] µ S [GeV] κ λ H H H [%] log 0 (Λ/GeV)

88 Benchmark points Z2-symmetric S S2 S3 S4 H-S mixing parameters λ HS λ HS,µ HS λ HS,µ HS µ HS PT type D B B B m H2 [GeV] α [degrees] v S [GeV] µ HS [GeV] µ S [GeV] κ λ H H H [%] log 0 (Λ/GeV)

89 Benchmark points Z2-symmetric S S2 S3 S4 H-S mixing parameters λ HS λ HS,µ HS λ HS,µ HS µ HS PT type D B B B m H2 [GeV] α [degrees] v S [GeV] µ HS [GeV] µ S [GeV] κ λ H H H [%] log 0 (Λ/GeV) excluded

90 Benchmark points Z2-symmetric S S2 S3 S4 H-S mixing parameters λ HS λ HS,µ HS λ HS,µ HS µ HS PT type D B B B m H2 [GeV] α [degrees] v S [GeV] µ HS [GeV] µ S [GeV] κ λ H H H [%] log 0 (Λ/GeV) excluded

91 Benchmark points Z2-symmetric S S2 S3 S4 H-S mixing parameters λ HS λ HS,µ HS λ HS,µ HS µ HS PT type D B B B m H2 [GeV] α [degrees] v S [GeV] µ HS [GeV] µ S [GeV] κ λ H H H [%] log 0 (Λ/GeV) excluded no significant deviation

92 Benchmark points Z2-symmetric S S2 S3 S4 H-S mixing parameters λ HS λ HS,µ HS λ HS,µ HS µ HS PT type D B B B m H2 [GeV] α [degrees] v S [GeV] µ HS [GeV] µ S [GeV] κ λ H H H [%] log 0 (Λ/GeV) excluded no significant deviation

93 Benchmark points Z2-symmetric S S2 S3 S4 H-S mixing parameters λ HS λ HS,µ HS λ HS,µ HS µ HS PT type D B B B m H2 [GeV] α [degrees] v S [GeV] µ HS [GeV] µ S [GeV] κ λ H H H [%] log 0 (Λ/GeV) below GUT scale excluded no significant deviation

94 light stop scenario m 2 t (') ' y2 t sin 2 2 MSSM EWBG ' 2 (m 2 q L m 2 t R, A t µ/ tan 2 ' 0) Strong st -order EWPT is driven by the light stop with a mass below 20 GeV. [M. Carena et al, NPB82, (2009) 243]. Prediction: (gg -> H -> VV)/ (gg -> H -> VV) SM (2-3) t t t

95 light stop scenario m 2 t (') ' y2 t sin 2 2 MSSM EWBG ' 2 (m 2 q L m 2 t R, A t µ/ tan 2 ' 0) Strong st -order EWPT is driven by the light stop with a mass below 20 GeV. [M. Carena et al, NPB82, (2009) 243]. Prediction: (gg -> H -> VV)/ (gg -> H -> VV) SM (2-3) t t t Confronting this scenario with LHC data, MSSM EWBG is ruled out at greater than 98% CL (ma> TeV), at least 90% CL for light value of ma (~300 GeV) [D. Curtin, P. Jaiswall, P. Meade., JHEP08(202)005] σ(gg -> H -> VV) is inconsistent.

96 light stop scenario m 2 t (') ' y2 t sin 2 MSSM EWBG Strong st ~ ~ ~ ~ ~ ~ W b χ / t -order EWPT is driven by the light 500 stop with a 0 c χ 0 b f f χ 0 t / t / t mass below 20 t χ 0 t production, t Status: ICHEP 204 GeV. [M. Carena et al, NPB82, (2009) 243]. 2 ' 2 (m 2 q L m 2 t R, A t µ/ tan 2 ' 0) 0 t W b χ L [ ], 2L [ ] - ~ 0 t χ Prediction: (gg -> H -> VV)/ (gg c 0L [ ] - 0 b f f χ 0L [ ], L [ ] 350 -> H -> VV) SM - (2-3) [GeV] m χ ATLAS Preliminary ~ t t χ ~ t t χ ~ t t χ ~ Observed limits All limits at 95% CL - L int = 20 fb 0L [406.22] L [ ] 2L [ ] Expected limits s=8 TeV - = 4.7 fb L int 0L [ ] L [ ] 2L [ ] s=7 TeV t m ~ L int t < m b /m c + m χ 0 c χ = 20.3 fb 0 - m ~ t < m b + m W + m χ 0 m ~ t < m t +m χ 0 t b f f χ 0 t 50 0 L int W b χ 0 = 20.3 fb - - = 4.7 fb L int - = 20 fb L int m~ t [GeV] Confronting this scenario with LHC data, MSSM EWBG is ruled out at greater than 98% CL (ma> TeV), at least 90% CL for light value of ma (~300 GeV) [D. Curtin, P. Jaiswall, P. Meade., JHEP08(202)005] σ(gg -> H -> VV) is inconsistent.

97 light stop scenario m 2 t (') ' y2 t sin 2 MSSM EWBG Strong st ~ ~ ~ ~ ~ ~ W b χ / t -order EWPT is driven by the light 500 stop with a 0 c χ 0 b f f χ 0 t / t / t mass below 20 t χ 0 t production, t Status: ICHEP 204 GeV. [M. Carena et al, NPB82, (2009) 243]. 2 ' 2 (m 2 q L m 2 t R, A t µ/ tan 2 ' 0) 0 t W b χ L [ ], 2L [ ] - ~ 0 t χ Prediction: (gg -> H -> VV)/ (gg c 0L [ ] - 0 b f f χ 0L [ ], L [ ] 350 -> H -> VV) SM - (2-3) [GeV] m χ ATLAS Preliminary ~ t t χ ~ t t χ ~ t t χ ~ Observed limits All limits at 95% CL - L int = 20 fb 0L [406.22] L [ ] 2L [ ] Expected limits s=8 TeV - = 4.7 fb L int 0L [ ] L [ ] 2L [ ] s=7 TeV t m ~ L int t < m b /m c + m χ 0 c χ = 20.3 fb 0 - m ~ t < m b + m W + m χ 0 m ~ t < m t +m χ 0 t b f f χ 0 t 50 0 L int W b χ 0 = 20.3 fb - - = 4.7 fb L int - = 20 fb L int m~ t [GeV] Confronting this scenario with LHC data, MSSM EWBG is ruled out at greater than 98% CL (ma> TeV), at least 90% CL for light value of ma (~300 GeV) [D. Curtin, P. Jaiswall, P. Meade., JHEP08(202)005] σ(gg -> H -> VV) is inconsistent. v C & not satisfied T C

98 4 Higgs doublets+singlets-extended MSSM Strong st -order EWPT is driven by the charged Higgs bosons. 400 hγγ 400 hhh m Φ ± [GeV] v c /T c =.0 µ γγ =0.78 strong st -order EWPT m Φ ± [GeV] % v c /T c =.0 +40% +30% strong st -order EWPT +20% λ hhh λ hhh SM =+0% m Φ 0[GeV] m Φ 0[GeV] If the EWPT is strong st order, [S. Kanemura, E.S., T. Shindou, T. Yamada, JHEP05 (203) 066] - μγγ is reduced by more than 20%, - hhh coupling is enhanced by more than 20%.

99 4 Higgs doublets+singlets-extended MSSM Strong st -order EWPT is driven by the charged Higgs bosons. 400 hγγ 400 hhh m Φ ± [GeV] v c /T c =.0 µ γγ =0.78 strong st -order EWPT m Φ ± [GeV] % µ +30% 340 γγ =.7 ± 0.27 (ATLAS) 320 µ 300 γγ = % strong st -order EWPT v c /T c =.0 +20% 0.23 (CMS) λ hhh λ hhh SM =+0% m Φ 0[GeV] m Φ 0[GeV] If the EWPT is strong st order, [S. Kanemura, E.S., T. Shindou, T. Yamada, JHEP05 (203) 066] - μγγ is reduced by more than 20%, - hhh coupling is enhanced by more than 20%.

100 Singlino-driven EWBG in the NMSSM [K. Cheung, TJ. Hou, JS. Lee, E.S., PLB70 (202) 88] Strong st -order EWPT is driven by the doublet-singlet mixing effects. CP-violation relevant to the BAU comes from Higgsino-singlino int

101 Singlino-driven EWBG in the NMSSM [K. Cheung, TJ. Hou, JS. Lee, E.S., PLB70 (202) 88] Strong st -order EWPT is driven by the doublet-singlet mixing effects. CP-violation relevant to the BAU comes from Higgsino-singlino int

102 Singlino-driven EWBG in the NMSSM [K. Cheung, TJ. Hou, JS. Lee, E.S., PLB70 (202) 88] Strong st -order EWPT is driven by the doublet-singlet mixing effects. CP-violation relevant to the BAU comes from Higgsino-singlino int [GeV] m ~ Sbottom pair production, b ATLAS - Ldt = 20. fb, All limits at 95% CL s=8 TeV b 0 Observed limit (± - CDF 2.65 fb - D0 5.2 fb - ATLAS 2.05 fb, SUSY theory Expected limit (± exp ) s=7 TeV ) ~ b 0 b forbidden [GeV] m b ~

103 Singlino-driven EWBG in the NMSSM [K. Cheung, TJ. Hou, JS. Lee, E.S., PLB70 (202) 88] Strong st -order EWPT is driven by the doublet-singlet mixing effects. CP-violation relevant to the BAU comes from Higgsino-singlino int [GeV] m ~ Sbottom pair production, b ATLAS - Ldt = 20. fb, All limits at 95% CL s=8 TeV b 0 Observed limit (± - CDF 2.65 fb - D0 5.2 fb - ATLAS 2.05 fb, SUSY theory Expected limit (± exp ) s=7 TeV ) ~ b 0 b forbidden [GeV] m b ~ This specific scenario is disfavored by sbottom searches.

104 Singlino-driven EWBG in the NMSSM [K. Cheung, TJ. Hou, JS. Lee, E.S., PLB70 (202) 88] Strong st -order EWPT is driven by the doublet-singlet mixing effects. CP-violation relevant to the BAU comes from Higgsino-singlino int [GeV] m ~ Sbottom pair production, b ATLAS - Ldt = 20. fb, All limits at 95% CL s=8 TeV b 0 Observed limit (± - CDF 2.65 fb - D0 5.2 fb - ATLAS 2.05 fb, SUSY theory Expected limit (± exp ) s=7 TeV ) ~ b 0 b forbidden [GeV] m b ~ This specific scenario is disfavored by sbottom searches. However, successful scenario still remain, e.g. bino-driven scenario.

105 Z -ino-driven EWBG in the UMSSM [E.S., PRD88, (203)] " Strong st -order EWPT is driven by the doublet-singlet mixing effects. " CP-violation relevant to the BAU comes from Higgsino-Z -ino int. " BAU can be explained if the Higgsino and Z -ino are nearly degenerate. " Predictions: g HVV =( ) and light leptophobic Z (<25 GeV)

106 Z -ino-driven EWBG in the UMSSM [E.S., PRD88, (203)] " Strong st -order EWPT is driven by the doublet-singlet mixing effects. " CP-violation relevant to the BAU comes from Higgsino-Z -ino int. " BAU can be explained if the Higgsino and Z -ino are nearly degenerate. " Predictions: g HVV =( ) and light leptophobic Z (<25 GeV)

107 Z -ino-driven EWBG in the UMSSM [E.S., PRD88, (203)] Strong st -order EWPT is driven by the doublet-singlet mixing effects. CP-violation relevant to the BAU comes from Higgsino-Z -ino int. BAU can be explained if the Higgsino and Z -ino are nearly degenerate. Predictions: g HVV =( ) and light leptophobic Z (<25 GeV)

108 Z -ino-driven EWBG in the UMSSM [E.S., PRD88, (203)] Strong st -order EWPT is driven by the doublet-singlet mixing effects. CP-violation relevant to the BAU comes from Higgsino-Z -ino int BAU can be explained if the Higgsino and Z -ino are nearly degenerate. Predictions: g HVV =( ) and light leptophobic Z (<25 GeV)

109 Z -ino-driven EWBG in the UMSSM [E.S., PRD88, (203)] Strong st -order EWPT is driven by the doublet-singlet mixing effects. CP-violation relevant to the BAU comes from Higgsino-Z -ino int BAU can be explained if the Higgsino and Z -ino are nearly degenerate. Predictions: g HVV =( ) and light leptophobic Z (<25 GeV)

110 Experimental constraints on light leptophobic Z Electroweak precision tests (see e.g. Umeda,Cho,Hagiwara, PRD58 (998) 5008) -> In our case, no constraint since Z-Z mixing is assumed to be small. All dijet-mass searches at Tevatron/LHC are limited to M jj >200 GeV. Z boson (<200 GeV) is constrained by the UA2 experiment. UA2 bounds on m Z UA2 Collaborations,NPB400: (993) 3 M. Buckley et al,prd83:503 (20) ~ UA g ffz fl,r µ f L,R Z µ 0 I,,,,I,,,H I,, M~/(GeV) Fig. 5. Excluded region to 90% for Z. ~q, (excluded region is hatched). The branching ratio is given as a fraction of standard model branching ratio. The solid line shows a branching ratio of for Z ~c~qwhilst the dashed line shows a branching ratio of 0.7.

111 Sphaleron s (sphaleros) ready to fall [F.R.Klinkhamer and N.S.Manton, PRD30, 222 (984)] Energy sphaleron vacuum NCS = vacuum NCS = 0

112 Sphaleron in the SU(2) gauge-higgs system L gauge+higgs = 4 F a µ F aµ +(D µ ) D µ V ( ) F a µ = µ A a A a µ + g 2 abc A b µa c, D µ = µ ig 2 A a µ 2 a, V( )= v We consider the static classical solution. E = d 3 x 4 F a ijf a ij +(D i ) D i + v 2 2 2, A 0 =0. Since lim x E = finite, A and must have the form of the vacuum configurations at x = : i A i (x) = iu(, )U (, ), g 2 (x) = U(, ) 0 v/ 2 where U(, ) such that S 2 SU(2) S 3.U( =0, )=.,

113 where Noncontractible loop parameter familiy U(µ,, ) (µ [0, ]) with finite E. [S S 2 S 3 ] U(µ,, ) = U(µ, +, )=U(µ,, +2 ), for µ, U(0,, ) = U(,, )=, U(µ, 0, )=, vacuum (µ,, ) S 3, U(µ,, ) is noncontractible since 3(SU(2)) Z. Energy sphaleron µ = /2 µ = vacuum NCS = saddle point = maximum energy along the least energy path -> =π/2 vacuum µ =0 vacuum -> =0,π. NCS = 0 U(µ,, )= eiµ (cos µ i sin µ cos ) e i sin µ sin e i sin µ sin e iµ (cos µ + i sin µ cos ).

114 Ansatz Let us consider the configuration space spanned by the following: A i (µ, x) = (µ, x) = U(µ,, ) i g 2 iu(µ,, )U (µ,, ), 0 v/ 2 in the limit of r = x = this space are. The most highest symmetry configurations in A i (µ, r,, ) = i g 2 f(r) i U(µ,, )U (µ,, ), (µ, r,, ) = v 2 ( h(r)) 0 e iµ cos µ + h(r)u(µ,, ) 0. µ = /2 saddle point configuration (spahaleron) cf. µ = 0, vacuum configuration

115 Change the variable r = x 2 to. Energy functional E sph = 4 v g 2 0 d 4 df d (f f 2 ) dh d 2 + h 2 ( f) 2 + 4g (h 2 ) 2 4 v g 2 E, where = g 2 vr. Equations of motion for the sphaleron d d d 2 d f( ) = 2 f( )( f( ))( 2f( )) h2 ( )( f( )), 2 dh( ) = 2h( )( f( )) 2 + (h 2 ( ) )h( ) d g 2 2 with the boundary conditions lim 0 f( )=0, lim 0 h( )=0, lim f( )=, lim h( )=.

116 Higgs couplings Table 9.. Summary of expected accuracies g i /g i for model independent determinations of the Higgs boson couplings. The theory errors are F i /F i =0.%. Fortheinvisiblebranchingratio,thenumbersquotedare95% confidence upper limits. Ô s (GeV) ILC(250) ILC(500) ILC(000) ILC(LumUp) L(fb ) % 8.4 % 4.0 % 2.4 % gg 6.4 % 2.3 %.6 % 0.9 % WW 4.8 %. %. % 0.6 % ZZ.3 %.0 %.0 % 0.5 % t t 4 % 3. %.9 % b b 5.3 %.6 %.3 % 0.7 % % 2.3 %.6 % 0.9 % c c 6.8 % 2.8 %.8 %.0 % µ + µ 9% 9% 6 % 0 % T (h) 2 % 4.9 % 4.5 % 2.3 % hhh 83 % 2 % 3 % BR(invis.) < 0.9 % < 0.9 % < 0.9 % < 0.4 % ILC can probe EWBG-favored region.

117 Measurement of hhh hhh can be measured by double Higgs productions. At linear collider: Higgsstrahlung e - e + Z Z h h λhhh h e- e + Z Z h h e - e+ Z Z h h e - e + W h W ν e h λ hhh h ν e e - e + WW-fusion W W W ν e h h ν e e e - + W W ν h e h ν e

118 e- Production cross sections Z Z * h * h e + hhh λhhh = λ SM hhh ( + κ), h FIG. 6: The full cross section of e e (γ(+)γ(+)) hh p GeV (left) and m h =60GeV(right). [E.Asakawa, D.Harada, S.Kanemura, Y.Okada, K.Tsumura, PRD82(200)5002] For s TeV, production cross section is O(0.)fb For s>tev, WW-fusion is also important. FIG. 7: The cross sections of e + e hhν ν process at th