H -> gamma gamma: a Comment on the Indeterminacy of Non-Gauge-Invariant Integrals

TL;DR

This paper examines the indeterminacy issues in calculating the Higgs to two photons decay amplitude using gauge-breaking regulators, highlighting the limitations of certain gauges and regularization schemes in obtaining consistent results.

Contribution

It clarifies the role of gauge invariance and regularization choices in the indeterminacy of Higgs decay amplitude calculations, especially in the unitary gauge.

Findings

Imposing gauge invariance restores the standard H -> gamma gamma result.

Unitary gauge with cutoff regularization is non-predictive due to indeterminacy.

Gauge invariance constraints can resolve integral ambiguities in R_xi gauges.

Abstract

We reanalyze the recent computation of the amplitude of the Higgs boson decay into two photons presented by Gastmans et al.. The reasons for which this result cannot be the correct one have been discussed in some recent papers. We address here the general issue of the indeterminacy of integrals with four-dimensional gauge-breaking regulators and to which extent it might eventually be solved by imposing physical constraints. Imposing gauge invariance as the last step upon R_xi gauge calculations with four-dimensional gauge-breaking regulators, allows indeed to recover the well known H -> gamma gamma result. However we show that in the particular case of the unitary gauge, the indeterminacy cannot be tackled in this same way. The combination of unitary gauge with a cutoff regularization scheme turns out to be non-predictive.