Renormalization group optimized λφ4 pressure at next-to-next-to-leading order

We investigate the renormalization group optimized perturbation theory (RGOPT) at the next-to-next-toleading 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.

Automated summary

The investigation of renormalization group optimized perturbation theory (RGOPT) at NNLO for thermal scalar field theory demonstrates efficient resummation and excellent convergence properties, significantly improving the renormalization scale dependence of thermodynamical quantities compared to standard perturbative expansions and other resummation methods. These results provide a useful first NNLO illustration for potential applications of this approach to more complex thermal QCD.