Resummation of Goldstone Infrared Divergences: A Proof to All Orders

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.