Resummation of Goldstone Infrared Divergences: A Proof to All Orders

Understand

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.