Gauge invariance of the $h^0\rightarrow\gamma\gamma$ amplitude

Abstract

We point out that the one-loop amplitude of the $h^0\rightarrow\gamma\gamma$ decay is gauge invariant owing to a particular relation between the trilinear couplings and the Higgs boson mass. This relation follows only from the gauge symmetry breaking pattern realized by the potential of the scalar fields and not on its specific form. This allows to justify the seemingly inconsistent calculation of the $h^0\rightarrow\gamma\gamma$ amplitude in the minimal supersymmetric model (MSSM) in which one takes the mass of the lighter Higgs boson from e.g. the one-loop effective potential.