Running Couplings in High-Temperature Effective Field Theory

TL;DR

This paper investigates the two-loop renormalization-group evolution of parameters in a three-dimensional effective field theory modeling the electroweak phase transition, including effects of beyond Standard Model physics and nonrenormalizable terms.

Contribution

It provides the first detailed two-loop calculations of running couplings in the 3D EFT with nonrenormalizable operators, crucial for accurate phase transition analysis.

Findings

Two-loop beta functions computed for 3D EFT couplings.

Impact of nonrenormalizable terms on phase transition dynamics analyzed.

Framework established for lattice simulation testing of higher-order effects.

Abstract

In this work, we study the renormalization-group evolution of parameters in the three-dimensional effective field theory (3D EFT) that describes the thermally driven electroweak phase transition of the Higgs field. We consider tree-level and radiatively generated barriers induced by beyond the Standard Model physics, enabling a first-order phase transition at and below the soft scale, respectively. For each case, we compute the two-loop running of the 3D EFT couplings, including the effects of the leading nonrenormalizable terms. We then analyze how the new contributions to the beta functions compare with those in the super-renormalizable case, highlighting their impact on perturbative computations of the scalar potential, which describes the vacuum structure of the theory. By incorporating higher-order corrections in the mass parameter evolution, as well as the running of other effective operators, we set the stage for testing their impact on phase transition dynamics in lattice simulations.