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

TL;DR

This paper examines how regularization-dependent parameters affect finite quantum amplitudes like Higgs decay and photon scattering, highlighting ambiguities and their relation to gauge invariance.

Contribution

It introduces a general parametrization of ultraviolet divergences that clarifies the origin of regularization ambiguities in finite quantum processes.

Findings

Regularization ambiguities can be separated into surface terms using Implicit Regularization.

Momentum routing invariance is shown to be equivalent to gauge invariance in the studied amplitudes.

Different regularization schemes can be understood within this framework, clarifying their impact on physical results.

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.