Higgs Decay into Two Photons through the W-boson Loop: No Decoupling in the m_W --> 0 Limit

TL;DR

This paper reexamines the Higgs decay into two photons via W-boson loops, demonstrating that the contribution persists even as the W-boson mass approaches zero, contradicting recent claims of decoupling.

Contribution

It clarifies that the W-boson loop contribution does not decouple in the massless limit, reaffirming the validity of traditional calculations and correcting recent misconceptions.

Findings

W-boson loop contribution remains nonzero as m_W --> 0

Longitudinal polarization coupling persists in the massless limit

Contradicts recent claims of decoupling in the literature

Abstract

We reanalyze the W-boson loop in the amplitude of the Higgs decay into two photons to show the absence of decoupling in the limit of massless W bosons, m_W --> 0. The Higgs coupling to longitudinal polarizations survive in this limit and generates a nonvanishing contribution in the $H\to \gamma\gamma$ decay. This shows that the recent claim of decoupling by R. Gastmans, S.L. Wu, and T.T. Wu is incorrect, and the old calculations for the two photon decay well known in the literature are valid.