Taming the Goldstone contributions to the effective potential

TL;DR

This paper addresses issues with the effective potential caused by Goldstone boson contributions, proposing a resummation method that removes divergences and unphysical imaginary parts, leading to more stable calculations.

Contribution

It introduces a resummation technique for Goldstone boson contributions that eliminates divergences and imaginary parts in the effective potential.

Findings

Resummation removes the imaginary parts caused by negative G.

The minimization condition becomes finite and well-defined.

The approach yields a stable effective potential without G dependence.

Abstract

The standard perturbative effective potential suffers from two related problems of principle involving the field-dependent Goldstone boson squared mass, G. First, in general G can be negative, and it actually is negative in the Standard Model; this leads to imaginary contributions to the effective potential that are not associated with a physical instability, and therefore spurious. Second, in the limit that G approaches zero, the effective potential minimization condition is logarithmically divergent already at two-loop order, and has increasingly severe power-law singularities at higher loop orders. I resolve both issues by resumming the Goldstone boson contributions to the effective potential. For the resulting resummed effective potential, the minimum value and the minimization condition that gives the vacuum expectation value are obtained in forms that do not involve G at all.