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

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.