Resummation of Goldstone Infrared Divergences: A Proof to All Orders

TL;DR

This paper proves that infrared divergences caused by Goldstone bosons in the effective potential can be systematically removed at all orders through a resummation technique that shifts the Goldstone mass, ensuring more reliable calculations.

Contribution

It provides a rigorous proof of the resummation method for Goldstone divergences to all orders using an effective theory approach and the method of regions.

Findings

Infrared divergences are spurious and removable by resummation.

A compact recipe for Goldstone mass shift is derived.

The proof applies to all loop orders in perturbation theory.

Abstract

The perturbative effective potential calculated in Landau gauge suffers from infrared problems due to Goldstone boson loops. These divergences are spurious and can be removed by a resummation procedure that amounts to a shift of the mass of soft Goldstones. We prove this to all loops using an effective theory approach, providing a compact recipe for the shift of the Goldstone mass that relies on the use of the method of regions to split soft and hard Goldstone contributions.