On the Standard Approach to Renormalization Group Improvement

TL;DR

This paper compares two methods of renormalization-group improvement—substituting running parameters versus summing leading logs—in the context of the effective potential in a massless scalar field theory, highlighting their differences at two-loop order.

Contribution

It provides a detailed comparison of the standard approaches to renormalization-group improvement, clarifying their distinctions at higher-loop orders in a specific quantum field theory model.

Findings

The two approaches differ at two-loop order when considering NLL contributions.

Systematic summation of logs captures different effects than substitution of running couplings.

The analysis clarifies the applicability and limitations of each method in quantum field theory calculations.

Abstract

Two approaches to renormalization-group improvement are examined: the substitution of the solutions of running couplings, masses and fields into perturbatively computed quantities is compared with the systematic sum of all the leading log (LL), next-to-leading log (NLL) etc. contributions to radiatively corrected processes, with n-loop expressions for the running quantities being responsible for summing N^{n}LL contributions. A detailed comparison of these procedures is made in the context of the effective potential V in the 4-dimensional O(4) massless $\lambda \phi^{4}$ model, showing the distinction between these procedures at two-loop order when considering the NLL contributions to the effective potential V.