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

TL;DR

This paper demonstrates that the one-loop amplitude for the decay of the Higgs boson into two photons is gauge invariant due to a fundamental relation derived from gauge symmetry breaking, applicable across various models.

Contribution

It establishes a gauge invariance proof for the $h^0 ightarrow\gamma\gamma$ amplitude based on symmetry relations, clarifying calculations in models like the MSSM.

Findings

The amplitude is gauge invariant due to a relation between couplings and Higgs mass.

This relation stems from the gauge symmetry breaking pattern, not the specific potential form.

Supports consistent calculations of Higgs decay amplitudes in supersymmetric models.

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.