Supersymmetric Electroweak Phase Transition: Dimensional Reduction versus Effective Potential

Abstract

We compare two methods of analyzing the finite-temperature electroweak phase transition in the minimal supersymmetric standard model: the traditional effective potential (EP) approach, and the more recently advocated procedure of dimensional reduction (DR). The latter tries to avoid the infrared instabilities of the former by matching the full theory to an effective theory that has been studied on the lattice. We point out a limitation of DR that caused a large apparent disagreement with the effective potential results in our previous work. We also incorporate wave function renormalization into the EP, which is shown to decrease the strength of the phase transition. In the regions of parameter space where both methods are expected to be valid, they give similar results, except that the EP is significantly more restrictive than DR for the range of baryogenesis-allowed values of $\tanβ$, $m_h$, the critical temperature, and the up-squark mass parameter $m_U$. In contrast, the DR results are consistent with $2\lsim\tanβ\lsim 4$, $m_h<80$ GeV, and $m_U$ sufficiently large to have universality of the squark soft-breaking masses at the GUT scale, in a small region of parameter space. We suggest that the differences between DR and EP are due to higher-order perturbative corrections rather than infrared effects.