Corrections to the electroweak effective action at finite temperature

We calculate contributions to the finite temperature effective action for the electroweak phase transition (EWPT) at [ital O]([ital g][sup 4]), i.e., at second order in ([ital g][sup 2][ital T]/[ital scrM]) and all orders in ([ital g][sup 2][ital T2]/[ital scrM][sup 2]). This requires plasma-mass corrections in the calculation of the effective potential, the inclusion of the lollipop'' diagram, and an estimate of derivative corrections. We find the EWPT remains too weakly first order to drive baryogenesis. We calculate some one-loop kinetic energy corrections using both functional and diagrammatic methods; these may be important for saddle point configurations such as the bounce or sphaleron.