  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.
