Effective Potential in Subleading Logarithmic Approximation in Arbitrary Non-renormalizable Scalar Field Theory

TL;DR

This paper extends the calculation of quantum corrections to the effective potential in scalar field theories to include subleading logarithmic terms, using a formalism applicable to both renormalizable and non-renormalizable models.

Contribution

It develops a method to sum leading and subleading logarithms in all orders of perturbation theory for arbitrary scalar potentials, including non-renormalizable theories.

Findings

Derived recurrence relations and RG equations for subleading logs.

Validated the formalism against a renormalizable model.

Applicable to arbitrary scalar potentials, regardless of renormalizability.

Abstract

Following the previously developed approach to the calculation of quantum corrections to the effective potential in arbitrary scalar field theories in the leading logarithmic approximation, we extended it to the next-to-leading order. Based on Bogoliubov-Parasiuk-Hepp-Zimmerman renormalization procedure and the Bogoliubov-Parasiuk theorem, we construct recurrence relations and renormalization group equations that allow one to sum up the leading and subleading logarithms in all orders of perturbation theory. The formalism is applicable to an arbitrary scalar potential, renormalizable or not. To verify the results, we compare them with a renormalizable model treated within the standard renormalization group approach.