Anatomy of the Higgs boson decay into two photons in the unitary gauge

TL;DR

This paper clarifies the calculation of the Higgs to two photons decay amplitude in the unitary gauge, resolving divergences and ambiguities through gauge invariance and equivalence theorems, and compares different regularisation schemes.

Contribution

It provides a four-dimensional method for computing the decay amplitude, resolving divergences without dimensional regularisation, and confirms consistency with established results.

Findings

Divergent integrals depend on shifting momenta choices.

A specific combination reduces divergence to logarithmic.

Agreement with dimensional regularisation results.

Abstract

In this work, we review and clarify computational issues about the W-gauge boson one-loop contribution to the H -> gamma gamma decay amplitude, in the unitary gauge and in the Standard Model. We find that highly divergent integrals depend upon the choice of shifting momenta with arbitrary vectors. One particular combination of these arbitrary vectors reduces the superficial divergency down to a logarithmic one. The remaining ambiguity is then fixed by exploiting gauge invariance and the Goldstone Boson Equivalence Theorem. Our method is strictly realised in four-dimensions. The result for the amplitude agrees with the "famous" one obtained using dimensional regularisation (DR) in the limit d-> 4, where d is the number of spatial dimensions in Euclidean space. At the exact equality d=4, a three-sphere surface term appears that renders the Ward Identities and the equivalence theorem inconsistent. We also examined a recently proposed four-dimensional regularisation scheme and found agreement with the DR outcome.