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

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.