SUSY and the Electroweak Phase Transition

We analyze the effective 3 dimensional theory previously constructed for the MSSM and multi-Higgs models to determine the regions of parameter space in which the electroweak phase transition is sufficiently strong for a B + L asymmetry to survive in the low temperature phase. We find that the inclusion of all supersymmetric scalars and all 1-loop corrections has the effect of enhancing the strength of the phase transition. Without a light stop or extension of the MSSM the phase transition is sufficiently first order only if the lightest Higgs mass Mh < ∼ 70 GeV and tanβ < ∼ 1.75. On leave of absence from Centro Internacional de F́ısica and Universidad Antonio Nariño, Santa Fe de Bogotá, COLOMBIA. For electroweak baryogenesis to occur it is necessary that the electroweak phase transition be sufficiently strongly first order. Otherwise, sphaleron transitions after the phase transition wash out any baryon asymmetry which may have been produced at the electroweak scale [1]. It is now known that this requirement is not satisfied in the minimal Standard Model [2, 3]. Thus, it is of interest to investigate extensions of the minimal Standard Model. Many authors have studied the order of the electroweak phase transition in the Minimal Supersymmetric Standard Model (MSSM). Most of these studies rely on a oneand two-loop finite-temperature effective potential analysis of the phase transition [4, 5, 6, 7, 8] in which stops were expected to make the most significant contribution from supersymmetric particles. The authors of these studies, in the limit of a large pseudoscalar Higgs mass, mA → ∞, have identified a region of parameter space for which the transition is strong enough. This corresponds to low values of tanβ, and values of the soft supersymmetry breaking right stop mass, m2U3 , which are small or even negative. In reference [6] the analysis was extended for the full range of allowed values of mA. It was found that larger values of mA are favored. A different approach consists of separating the perturbative and nonperturbative aspects of the phase transition. This is performed through the perturbative construction of effective three dimensional theories, and a subsequent lattice analysis of the reduced theory [2, 3, 9, 10]. For the case in which the reduced theory contains a single light Higgs field, characterized by a Higgs self-coupling, λ̄3, and an effective 3D gauge coupling, g3, the condition for a sufficiently strong first order phase transition becomes [2] xc = λ̄3 g 3 < ∼ 0.04, (1) where the quantities λ̄3 and g3 are functions of the various parameters appearing in the original 4D theory. An analysis of the parameter space for the reduced theory of the Standard