Higgs-Photon-Photon Amplitude in the Unitary Gauge

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.