First Order Phase Transition in a Two Higgs-doublet Model with Mₕ>MW

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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-ε 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.