Note on Higgs Decay into Two Photons $H\to \gamma\gamma$

TL;DR

This paper revisits the Higgs decay into two photons via W-loop in the unitary gauge, employing a symmetry-preserving regularization method to ensure gauge invariance and clarify previous discrepancies in the literature.

Contribution

It introduces a loop regularization scheme in four dimensions that preserves gauge invariance and clarifies the non-decoupling behavior in Higgs decay calculations.

Findings

Confirmed the non-decoupling effect in $H o \gamma\gamma$ decay.

Resolved discrepancies between earlier results and recent literature.

Demonstrated the advantage of the unitary gauge in analyzing gauge boson contributions.

Abstract

The Higgs decay $H\to \gamma\gamma$ duo to the virtual $W$-loop effect is revisited in the unitary gauge by using the symmetry-preserving and divergent-behavior-preserving loop regularization method, which is realized in the four dimensional space-time without changing original theory. Though the one-loop amplitude of $H\to \gamma\gamma$ is finite as the Higgs boson in the standard model has no direct interaction with the massless photons at tree level, while it involves both tensor-type and scalar-type divergent integrals which can in general destroy the gauge invariance without imposing a proper regularization scheme to make them well-defined. As the loop regularization scheme can ensure the consistency conditions between the regularized tensor-type and scalar-type divergent irreducible loop integrals to preserve gauge invariance, we explicitly show the absence of decoupling in the limit $M_W/M_H\to0$ and obtain a result agreed exactly with the earlier one in the literature. We then clarify the discrepancy between the earlier result and the recent one obtained by R. Gastmans, S.L. Wu and T.T. Wu. The advantage of calculation in the unitary gauge becomes manifest that the non-decoupling arises from the longitudinal contribution of the $W$ gauge boson.