(Un)determined finite regularization-dependent quantum corrections: The Higgs boson decay into two photons and the two-photon scattering examples

Abstract

We investigate the appearance of arbitrary, regularization-dependent parameters introduced by divergent integrals in two a priori finite but superficially divergent amplitudes: the Higgs decay into two photons and the two-photon scattering. We use a general parametrization of ultraviolet divergences which makes explicit such ambiguities. Thus we separate in a consistent way using implicit regularization the divergent, finite, and regularization-dependent parts of the amplitudes which in turn are written as surface terms. We find that, although finite, these amplitudes are ambiguous before the imposition of physical conditions, namely, momentum routing invariance in the loops of Feynman diagrams. In the examples we study, momentum routing invariance turns out to be equivalent to gauge invariance. We also discuss the results obtained by different regularizations and show how they can be reproduced within our framework allowing for a clear view on the origin of regularization ambiguities.