Renormalization group optimized $\lambda \phi^4$ pressure at next-to-next-to-leading order

TL;DR

This paper applies the renormalization group optimized perturbation theory at NNLO to thermal scalar field theory, demonstrating improved convergence and reduced scale dependence, paving the way for future thermal QCD studies.

Contribution

It provides the first NNLO application of RGOPT to thermal scalar field theory, showing enhanced resummation efficiency and convergence compared to previous methods.

Findings

Significant reduction in renormalization scale dependence.

Demonstrated improved convergence properties of RGOPT at NNLO.

Established groundwork for applying NNLO RGOPT to thermal QCD.

Abstract

We investigate the renormalization group optimized perturbation theory (RGOPT) at the next-to-next-to-leading order (NNLO) for the thermal scalar field theory. From comparing three thus available successive RGOPT orders we illustrate the efficient resummation and very good apparent convergence properties of the method. In particular the remnant renormalization scale dependence of thermodynamical quantities is drastically improved as compared to both standard perturbative expansions and other related resummation methods, such as the screened perturbation theory. Our present results thus constitute a useful first NNLO illustration in view of NNLO applications of this approach to the more involved thermal QCD.