Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops

TL;DR

This paper develops a method to eliminate infra-red divergences caused by Goldstone bosons in two-loop effective potential calculations, enabling more accurate and efficient mass determinations in general field theories.

Contribution

It extends resummation techniques to general theories, providing compact, infra-red finite expressions and an on-shell Goldstone condition for two-loop calculations.

Findings

Infra-red divergences are avoided in the effective potential at two loops.

The method simplifies Higgs mass calculations by avoiding differential equations.

Results are applicable to a wide class of general renormalisable theories.

Abstract

We show how the infra-red divergences associated to Goldstone bosons in the minimum condition of the two-loop Landau-gauge effective potential can be avoided in general field theories. This extends the resummation formalism recently developed for the Standard Model and the MSSM, and we give compact, infra-red finite expressions in closed form for the tadpole equations. We also show that the results at this loop order are equivalent to (and are most easily obtained by) imposing an "on-shell" condition for the Goldstone bosons. Moreover, we extend the approach to show how the infra-red divergences in the calculation of the masses of neutral scalars (such as the Higgs boson) can be eliminated. For the mass computation, we specialise to the gaugeless limit and extend the effective potential computation to allow the masses to be determined without needing to solve differential equations for the loop functions -- opening the door to fast, infra-red safe determinations of the Higgs mass in general theories.