On the fate of the Standard Model at finite temperature

TL;DR

This paper updates the calculation of the electroweak vacuum stability in the Standard Model at finite temperature, incorporating higher-order corrections and thermal effects to refine the bounds on the top quark mass.

Contribution

It provides a more precise analysis of the thermal stability of the Standard Model vacuum using advanced loop calculations and numerical solutions of the bounce equation.

Findings

Finite temperature effects tighten the stability bound on the top quark mass.

The stability bound at high temperature is approximately 173.6 GeV for the top mass.

The analysis includes the impact of early Universe reheating on vacuum stability.

Abstract

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.