(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.

To $${d}$$ d , or not to $${d}$$ d : recent developments and comparisons of regularization schemes

“…Similar analyses, in many different theories and contexts, have been carried out in Refs. [78][79][80][81][82][83][84][85][86][87][88][89][90][91].…”

Computation of $$H\rightarrow gg$$ H → g g in fdh and dred: renormalization, operator mixing, and explicit two-loop results

“…Therefore, in fdh and dred it is not possible to derive complete results for the operator mixing analogous to Eqs. (12) and (13).…”

“…Purely four-dimensional schemes such as implicit regularization [9,10] and FDR [11] have been proposed and used to compute processes of practical interest such as H → γ γ [12,13] and H → gg [14]. The present paper is devoted to regularization by dimensional reduction (dred) [15] and the related four-dimensional helicity (fdh) scheme [16].…”

One-loop conformal anomaly in an implicit momentum space regularization framework

“…6. The ambiguity in the a term may be due to surface terms because they are often the source of ambiguities as we found in other models [50,51,53].…”