Two Higgs doublet dynamics at the electroweak phase transition: a non-perturbative study

Using a three-dimensional (3d) effective field theory and non-perturbative lattice simulations, we study the MSSM electroweak phase transition with two dynamical Higgs doublets. We first carry out a general analysis of spontaneous CP violation in 3d two Higgs doublet models, finding that this part of the parameter space is well separated from that corresponding to the physical MSSM. We then choose physical parameter values with explicit CP violation and a light right-handed stop, and determine the strength of the phase transition. We find a transition somewhat stronger than in 2-loop perturbation theory, leading to the conclusion that from the point of view of the non-equilibrium constraint, MSSM electroweak baryogenesis is allowed even for Higgs masses in excess of m_H = 110 GeV. Such values are experimentally viable at least if the mass parameter m_A is not too large, < 120 GeV, corresponding physically to m_{H+-} < 150 GeV. We find that a small m_A does not weaken the transition noticeably for a light enough stop. Finally we determine the properties of the phase boundary.