RG-Improved Three-Loop Effective Potential of the Massive $\phi^4$ theory

TL;DR

This paper applies the renormalization group method to the three-loop effective potential of massive f^4 theory, achieving next-next-next-to-leading logarithm resummation in the f MS scheme.

Contribution

It introduces a novel three-loop level resummation technique for the effective potential using four-loop RG functions in f^4 theory.

Findings

Achieved three-loop effective potential with resummed logarithms.

Utilized four-loop RG functions to improve accuracy.

Enhanced understanding of the f^4 theory's effective potential.

Abstract

The renormalization group method is applied to the three-loop effective potential of the massive $\phi^4$ theory in the $\bar{\rm MS}$ scheme in order to obtain the next-next-next-to-leading logarithm resummation. For this, we exploit four-loop parts of the renormalization group functions $\beta_\lambda$, $\gamma_m$, $\gamma_\phi$, and $\beta_\Lambda$, which were already given to five-loop order via the renormalization of the zero-, two-, and four-point one-particle-irreducible Green's functions, to solve evolution equations for the parameters $\lambda$, $m^2$, $\phi$, and $\Lambda$ within the accuracy of the three-loop order.