Renormalization group improvement of the effective potential in massive $\phi^4$ theory

TL;DR

This paper applies the renormalization group method to enhance the effective potential in massive 3f^4 theory, achieving higher-order logarithmic corrections consistent with known four-loop results.

Contribution

It introduces a renormalization group approach to improve the two-loop effective potential, capturing next-next-to-leading logarithmic corrections in the 3f^4 theory.

Findings

Successfully reproduces four-loop order logarithmic corrections

Provides a systematic method for higher-order effective potential calculations

Enhances understanding of quantum corrections in scalar field theories

Abstract

Using the method of renormalization group, we improve the two-loop effective potential of the massive $\phi^4$ theory to obtain the next-next-to-leading logarithm correction in the $\bar{MS}$ scheme. Our result well reproduces the next-next-to-leading logarithm parts of the ordinary loop expansion result known up to the four-loop order.