Comment on H --> gamma gamma and the role of the decoupling theorem and the equivalence theorem

TL;DR

This paper discusses the calculation of the Higgs to gamma gamma decay rate, emphasizing the importance of the equivalence theorem and the missing contributions from longitudinal W bosons in recent calculations.

Contribution

It highlights the omission of the longitudinal W boson contributions in recent calculations of the H --> gamma gamma decay rate, stressing the role of the equivalence theorem.

Findings

The longitudinal W boson contribution dominates in the heavy Higgs limit.

Omission of charged Higgs ghost contributions leads to incomplete decay rate calculations.

The equivalence theorem is crucial for accurate high-mass Higgs decay predictions.

Abstract

I am commenting on the paper Gastmans, Wu and Wu, which recently obtained new support by a paper by Christova and Todorov, about a new calculation of the H --> gamma gamma rate mediated by the W boson loop, and the lack of decoupling of the heavy states which mediate the decay. We remind the reader that the heavy Higgs limit is dominated by the contribution from the longitudinal W bosons, which in the limit m_H >> M_W are represented by the charged Higgs ghosts according to the equivalence theorem. The corresponding contribution is missing in Gastmans, Wu and Wu as well as in the new paper by Christova and Todorov.