Higgs boson decay into two photons through the W-boson loop: No decoupling in the m _W→0 limit

We reanalyze the W-boson loop in the amplitude of the Higgs boson 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 survives in this limit and generates a nonvanishing contribution in the H→γγ 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.