Renormalization Group Determination of the Five-Loop Effective Potential for Massless Scalar Field Theory

TL;DR

This paper calculates the five-loop effective potential for massless scalar field theory using renormalization-group methods, focusing on scheme conversion from MS to Coleman-Weinberg to improve theoretical precision.

Contribution

It provides the first five-loop effective potential calculation for massless scalar theory in the Coleman-Weinberg scheme, including scheme conversion techniques.

Findings

Five-loop effective potential computed in Coleman-Weinberg scheme

Summation of subleading logarithms achieved at five loops

Scheme conversion from MS to Coleman-Weinberg performed successfully

Abstract

The five-loop effective potential and the associated summation of subleading logarithms for O(4) globally-symmetric massless $\lambda\phi^4$ field theory in the Coleman-Weinberg renormalization scheme $\frac{d^4V}{d\phi^4}|_{\phi = \mu} = \lambda$ (where $\mu$ is the renormalization scale) is calculated via renormalization-group methods. An important aspect of this analysis is conversion of the known five-loop renormalization-group functions in the minimal-subtraction (MS) scheme to the Coleman-Weinberg scheme.