First Order Phase Transition in a Two Higgs-doublet Model with M_(h)>M_(W)

We study the 3d effective field theory of a weakly coupled two Higgs-doublet scalar model at high temperature. Our model has three scalar quartic couplings and an $O(4)$ symmetry which is spontaneously broken by a nonzero scalar field $vev$ at zero temperature. Using high temperature perturbation theory, renormalization group arguments in $4-\epsilon$ dimensions, as well as $1/N$ expansion techniques in 3 dimensions, we argue that the transition from the high temperature symmetry restoring phase to the low temperature phase is first order for a range of scalar couplings. This result is not due to gauge couplings. We discuss the implications of our results for baryogenesis in the two Higgs-doublet electroweak model, especially when the lightest neutral Higgs is heavier than the W--bosons.