Refined renormalization group improvement for thermally resummed effective potential

TL;DR

This paper introduces a new renormalization group improvement method for thermally resummed effective potentials, significantly reducing scale dependence and improving the accuracy of phase transition predictions.

Contribution

The authors develop a consistent RG improvement framework for thermally resummed perturbation theories, enhancing the precision of phase transition calculations.

Findings

Reduced scale dependence of critical temperature calculations.

Resummed one-loop potential aligns with two-loop results within errors.

Method effectively incorporates large logarithmic and power corrections.

Abstract

We newly develop a renormalization group (RG) improvement for thermally resummed effective potentials. In this method, $\beta$-functions are consistently defined in resummed perturbation theories, so that order-by-order RG invariance is not spoiled after thermal resummation. With this improvement, scale dependences of phase transition quantities such as a critical temperature, which are known to be notoriously large at the one-loop order, are greatly reduced compared to calculations with the conventional $\overline{\text{MS}}$ scheme. By taking advantage of the RG invariance, we also devise a resummation method that can incorporate potentially harmful large logarithmic terms and temperature-dependent power corrections in a generic form. We point out that a resummed one-loop effective potential refined by the method can give results that agree with those obtained by resummed two-loop effective potentials within errors.