On the fate of the Standard Model at finite temperature

In this paper we revisit and update the computation of thermal corrections to the stability of the electroweak vacuum in the Standard Model. At zero temperature, we make use of the full two-loop effective potential, improved by three-loop beta functions with two-loop matching conditions. At finite temperature, we include one-loop thermal corrections together with resummation of daisy diagrams. We solve numerically---both at zero and finite temperature---the bounce equation, thus providing an accurate description of the thermal tunneling. Assuming a maximum temperature in the early Universe of the order of $10^{18}$ GeV, we find that at finite temperature the instability bound excludes values of the top mass $M_t \gtrsim 173.6$ GeV, with $M_h \simeq 125$ GeV and including uncertainties on the strong coupling. We discuss the validity and temperature-dependence of this bound in the early Universe, with a special focus on the reheating phase after inflation.