RadCor: September 15, C.E.M. Wagner. Argonne National Laboratory. Research Λ done in collaboration with M. Carena #, J.

Transkript

1 RadCor: September 15, 2000 ELECTROWEAK BARYOGENESIS IN THE MSSM C.E.M. Wagner Argonne National Laboratory Research Λ done in collaboration with M. Carena #, J. Ellis, H. Haber, S. Heinemeyer, W. Hollik, S. Mrenna, J. Moreno #, A. Pilaftsis, M. Quiros #, M. Seco # and G. Weiglein Outline: 1. Introduction 2. Higgs Boson and Stop Masses and Electroweak Baryogenesis 3. Higgs Physics and CP-Violation 4. CP-violating currents and the Baryon Asymmetry 5. Conclusions Λ [hep-ph/ ,/ ,/ ,/ ]; # to appear

2 I. Introduction ffl Observable Universe presents a clear asymmetry between Matter and Anti-Matter N B fl N μb ffl Cosmic Rays: N μp ' 10 4 N P ffl Consistent with secondary emmision of P μ ffl No fl-ray sources in cluster of galaxies ffl What is the origin of the baryon asymmetry? ffl Sakharov Requirements Baryon Number Violation Any Baryon Number conserving process N B = N μb C and CP Violation (N B ) L;R 6= (N μb ) L;R Departure from Thermal Equilibrium. In thermal equilibrium N B = N μb

3 ffl In S.M. Baryon Number violation mediated by Non-Trivial Topological Configurations (Instantons) B = L ffl Rate exponentially suppressed at T = 0 (T = 0) ' exp( 2ß=ff W ) ' ffl At finite Temperaure, instead, ' fi 0 T exp( E sph (T )=T ) with E sph ' 8ßv(T )=g, and v(t ) being the v.e.v. of the Higgs field. ffl If n B = 0 for T > T c, independently of the source of baryon asymmetry n B s = nb s T c exp» 1016 T c [GeV ] exp E sph(t c ) T c ffl Therefore, for the preservation of the generated n B, v(t c ) T c 1

4 Finite Temperature Effective Potential V (ffi; T ) = V 0 (ffi) + V 1 (ffi; 0) + V 1 (ffi; T ) where the finite T contribution is given by X» ni m 2 i (ffi)t 2 V 1 (ffi; T ) = im 4 i (ffi) 48 64ß 2 X b i=b;f m 3 b(ffi)t 12ß log m 2 i (ffi) T 2 where i = n i ( 1) 2S and m i (ffi)» 2T. For large values of the particle masses, m(ffi) fl 2T, the finite T -contributions are exponentially suppressed. V (T ) = D(T 2 T 2 0 )ffi2 E B Tffi 3 + (T ) 2 ffi4 v(t c ) T c ' E B = (T c ) ffl In the SM, E B ' p 2(2M 3 W + M 3 Z )=(3ßv3 ), while m 2 H ' 2 v2. The condition of preservation of the generated baryon number v(t c ) T c 1 implies m H» 40GeV; ffl Electroweak Baryogenesis in the SM is ruled out.

5 EW Baryogenesis implies presence of new light boson degrees of freedom, with relevant couplings to the Higgs field. The Higgs boson should remain light. ffi(t c ) T c ' E B (T c ) ' X b n b g 3 bh v 2 m 2 H ffl Supersymmetry provides a natural framework for this scenario. Relevant Light Bosons: Supersymmetric Partners of the top quark (stops). Espinosa,Quiros, Zwirner 93; Carena,Quiros,Wagner 96 ffl Each stop has six degrees of freedom, and couplings of order one to the Higgs field. E B ' g3 W 4ß + h3 t 2ß ' 8 E SM and hence, Higgs masses up to GeV can be accomodated within the SUSY framework. ffl In the MSSM, there are two Higgs doublets H 1, H 2 and the left-handed and right-handed stop mix 2 M 2 ~t = 4 m2 Q + m 2 t + D L m t X t m t Xt Λ m 2 U + m 2 t + D R where m t = h t H 2, X t = A t μ Λ = tan fi and tan fi = H 2 =H

6 ffl For m Q fl m U, jx t j, and either for large values of the heavy Higgs doublet mass, m A fl M Z,orfor large tan fi, for most values of m A, there is one Higgs boson h with mass ψ m 2 t ~ 1 m 2 t~ 2 " m 2 h ' MZ 2 cos 2 2fi + 3m4 t 8ß 2 v 2 log + 2 jx tj 2 m 2 Q! m 2 t logψ ~ 1 m 2 + O ~t 2 ψ jxt j 4 m 4 Q m 4 t!#! ffl For m ~t1 ' m Q ' 1 TeV, m ~t2 ' m t and jx t j» 0:6m Q [g 2 ~th = h2 t (1 jx t j2 m 2 Q m h» 110 GeV The largest values of the Higgs boson mass are obtained for values of tan fi 5. In order to make a precise analysis, we should take into account Two loop corrections at zero and finite T. Finite two-loop corrections, ingnored here, can vary m h by a few GeV M. Carena, H. Haber, S. Heinemeyer, G. Weiglein and C. Wagner 00 Study of vacuum stability at zero and finite T. )],

7 Stop and Higgs Mass Predictions Carena, Quiros, Wagner 98 ffl X t (tan fi) grows to the left (top) of figure ffl Bound m < h ο 115 GeV obtained for m Q = 2 3 TeV. ffl Metastability possible if lifetime of metastable vacuum larger than age of the Universe.

8 The LEP Collider at CERN has reported a bound on the Standard Model Higgs mass of m > H ο 112 GeV at 95 % C.L. A 2.6 ff excess of events consistent with a SM-like Higgs boson, with mass of about GeV has also been reported. Great news! What would happen if bound increases to 115 GeV? ffl Bound is only valid for a SM-like Higgs. In the MSSM, m h behaves as a SM Higgs only for m A fl M Z. ffl Low values of m A decrease v(t c )=T c for small values of tan fi. ffl Low values of m A decrease m h for small values of tan fi, without affecting the Higgs couplings in a significant way. ffl The scenario of EW Baryogenesis in the MSSM can only survive if Value of tan fi is large, tan fi 5 and either Λ The excess of events observed at LEP correspond to a SM-like Higgs boson of mass in the range GeV!, or Λ The value of m A ' GeV.

9 If all Higgs bosons are light, these particles may escape detection because either ffl Their couplings to the gauge bosons are suppressed and/or ffl Their couplings to b-quarks are suppressed In the presence of CP-violating phases of the SUSY parameters, the three neutral Higgs boson mix and their couplings X to the Z-boson fulfill i g 2 H i ZZ = 1; g H i ZZ = ffl ijk g Hj H k Z M. Carena, J.Ellis, A.Pilaftsis and C. Wagner 99, 00 Moreover, the couplings of the Higgs bosons to b-quarks may be strongly affected by radiative corrections.

10 Higgs Properties vs. arg(a t μ) M H1, M H2 [ GeV ] M H + = 200 GeV, tanβ = 25 µ = 1 TeV, A t = 0.35 TeV, A b = 0.5 TeV m(gluino) = 0.5 TeV, m(wino) = m(bino) = 0.2 TeV arg (A t ) = arg (A b ) [ deg ] (a) (g S H1bb )2 + (g P H1bb ) arg (A t ) = arg (A b ) [ deg ] (b) M. Carena, J. Ellis, A. Pilaftsis and C.W. 00 ffl Dashed- and solid-lines correspond to gluino mass phase arg(m ~g ) = 0 and ß, respectively.

11 Suppression of coupling of Higgs to b-quarks and Tevatron Reach m stop =200 GeV, A t =.65 TeV, µ= 1 TeV,W/Zh bb 5 fb fb fb fb -1 tanβ CDF and D0 Detectors M A (GeV) M. Carena, S. Mrenna and C.W. 99

12 Computation of Baryon Asymmetry M. Carena, M. Quiros, M. Seco and C.W., to appear ffl We derived difussion equations for the chiral charges induced by the passage of the wall of the expanding true-vacuum bubbles. ffl We developed a method to compute the CP-Violating sources of baryon asymmetry in a derivative expansion, to all orders in Higgs mass insertions. ffl Sources are dominated by chargino-neutralino contributions, and proportional to arg(m 2 μ), where M 2 and μ are the masses of the supersymmetric partners of the gauge and the Higgs boson fields, respectively. ffl Results depend slightly on the wall parameters and strongly on M 2, jμj and m A. The results also depend linearly on arg(m 2 μ). ffl Results generalize the previously found ones M. Carena, M. Quiros, A. Riotto, I. Vilja and C.W. 98

13 Baryon Asymmetry for arg(m 2 μ) = ß=2 60 M 2 = µ 40 m A = 100 GeV m A = 200 GeV m A = 300 GeV η/η BBN µ (GeV) ffl We set v(t c )=T c 1; tan fi = 5 20, m h ' GeV for m Q = 1 3 TeV. Gaugino masses of order of the weak scale. Larger jμj suppresses n B : n B ' n 0 B fi μ0 μ fi 2.

14 Conclusions ffl The scenario of Electroweak Baryogenesis can be realized in the MSSM if m h < ο GeV, m ~t < m t ffl Present LEP bounds imply that if this scenario is realized if Large values of tan fi > 5 and Large values of m Q = 1 3 TeV. Small values of m H + Higgs at LEP. < 300 GeV preferred if no ffl Computation of Baryon asymmetry: Acceptable values of = BBN for arg(m 2 μ) 0:01. ffl Values of the gaugino and Higgsino masses of order of the weak scale are preferred. ffl If Higgs bosons are not seen at LEP due to kinematic reasons or a suppression of its coupling to b-quarks, they should be seen at either a high luminosity Tevatron or at the LHC (H! flfl). ffl Light stops, and probably light charginos should also be seen at at least one of these colliders.