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 $O\left(g^4\right)$, i.e., at second order in ($\frac{g^{2}T}{\mathcal{M}}$) and all orders in ($\frac{g^2{T}^2}{{\mathcal{M}}^2}$). 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.