Higgs-Photon-Photon Amplitude in the Unitary Gauge

TL;DR

This paper demonstrates that the one-loop Higgs to two photons amplitude in the Standard Model is gauge invariant when using dimensional regularization, confirming consistency across different gauges.

Contribution

It proves the gauge invariance of the Higgs to two photons amplitude in the unitary gauge using dimensional regularization, clarifying previous ambiguities.

Findings

The amplitude is gauge invariant with dimensional regularization.

The amplitude in the unitary gauge matches that in the Feynman gauge.

The result resolves confusion over gauge invariance in this process.

Abstract

The physical process of Higgs decaying to two photons is the most important mode in the discovery of the Higgs particle. Theoretical calculation of $H\rightarrow\gamma\gamma$ amplitude therefore provides us with an avenue to explore the underlying theory. Yet some confusion has arisen over the gauge invariant property of $H\rightarrow\gamma\gamma$ in the standard model. In this paper, we show that if dimensional regularization is adopted, the on-shell 1-loop $H\rightarrow\gamma\gamma$ amplitude calculated in the standard model is gauge invariant. In particular, we prove that the physical amplitude calculated in the unitary gauge is the same as that calculated in the Feynman gauge.