  The imaginary part of the Feynman amplitude of the $W$-loop contribution to
the Higgs decay into two gammas (viewed as a function of the square of the off
shell Higgs momentum) is finite and unambiguous. It is presented as the product
of an invariant amplitude ${\cal A}$ times a bilinear in the components of the
(on shell) photon momenta factor which takes the Ward identity into account.
The unsubtracted dispersion integral of ${\cal A}$ is convergent and reproduces
the amplitude computed by R. Gastmans, S.L. Wu and T.T. Wu [GWW]. In
particular, the decoupling theorem, criticized as an unjustified assumption in
a subsequent paper [SVVZ12], is obtained as a corollary. By contrast with the
currently used value (computed in [SVVZ]) our calculation provides a smaller
Higgs decay rate into 2 photons than the currently observed. If accepted as a
true prediction of the Standard Model, it would be a first indication for the
need of a New Physics.
