Higher-order corrections to phase-transition parameters in dimensional reduction

TL;DR

This paper investigates how higher-order corrections in dimensional reduction affect the parameters of phase transitions in quantum field theories, revealing significant impacts on gravitational wave signals and extending computational methods for bounce solutions.

Contribution

It provides a quantitative analysis of higher-order interactions on phase transition parameters and derives equations for bounce solutions with higher-derivative terms.

Findings

Higher-order corrections expand the parameter space for strong phase transitions.

Peak frequency and amplitude of gravitational waves can vary by over an order of magnitude.

New equations for bounce solutions with higher-derivative terms are derived.

Abstract

The dynamics of phase transitions (PT) in quantum field theories at finite temperature is most accurately described within the framework of dimensional reduction. In this framework, thermodynamic quantities are computed within the 3-dimensional effective field theory (EFT) that results from integrating out the high-temperature Matsubara modes. However, strong-enough PTs, observable in gravitational wave (GW) detectors, occur often nearby the limit of validity of the EFT, where effective operators can no longer be neglected. Here, we perform a quantitative analysis of the impact of these interactions on the determination of PT parameters. We find that they allow for strong PTs in a wider region of parameter space, and that both the peak frequency and the amplitude of the resulting GW power spectrum can change by more than one order of magnitude when they are included. As a byproduct of this work, we derive equations for computing the bounce solution in the presence of higher-derivative terms, consistently with the EFT power counting.