Once more on the W-loop contribution to the Higgs decay into two photons

Abstract

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 $\mathcal{A}$ 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 $\mathcal{A}$ 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.

Comments: new discussions added at the end of Sec.3, 3 references added, changes at the end of the Abstract