A renormalization group improvement for thermally resummed effective potential

TL;DR

This paper introduces a new renormalization group improvement method for thermally resummed effective potentials, reducing scale dependence and enabling higher-order corrections in finite-temperature quantum field theory.

Contribution

It presents a temperature-dependent renormalization scheme that maintains RG invariance order by order, improving the accuracy of phase transition predictions.

Findings

Mitigates renormalization scale dependence of critical temperature

Maintains RG invariance at each order in resummed perturbation theory

Provides a practical method to include higher-order thermal corrections

Abstract

We propose a novel method for renormalization group improvement of thermally resummed effective potential. In our method, $\beta$-functions are temperature dependent as a consequence of the divergence structure in resummed perturbation theory. In contrast to the ordinary $\overline{\text{MS}}$ scheme, the renormalization group invariance of the resummed finite-temperature effective potential holds order by order, which significantly mitigates a notorious renormalization scale dependence of phase transition quantities such as a critical temperature even at the one-loop order. We also devise a tractable method that enables one to incorporate temperature-dependent higher-order corrections by fully exploiting the renormalization group invariance.