Towards the finite quantum field theory

TL;DR

This paper introduces a new regularization and renormalization scheme using auxiliary Feynman parameterization, achieving finite quantum field theories and matching standard results while providing novel insights into anomalies and divergences.

Contribution

A novel regularization scheme utilizing auxiliary Feynman parameters that yields finite quantum field theories and aligns with dimensional renormalization results.

Findings

Renormalized diagrams match dimensional renormalization except for counterterms.

Finite QCD supports experimental data on effective charge.

The scheme effectively handles anomalies and overlapping divergences.

Abstract

In this study, we propose a novel regularization/renormalization scheme that utilizes an auxiliary Feynman parameterization. This approach is employed to align a specified loop diagram with a designated unit of the form $1=\lambda/\lambda$. Within the proposed regularization technique, we formulate the standard renormalization scheme and demonstrate conditions under which it yields symmetry preserving results. It is demonstrated that its minimal form yields renormalized diagrams that are equivalent to those of the dimensional renormalization scheme, with the exception of their counterterms. Furthermore, a novel procedure for taking the soft limit $\lambda\rightarrow 0$, where a properly defined order of computational actions provides the field theory completely finite, is presented.The qualitative and quantitative distinctions between this approach and the standard scheme are highlighted. Both schemes are elucidated in the scalar model in 3+1D for pedagogical reasons. Subsequently, the proposed schemes are applied to the Standard Model at one loop level, e.g. we calculate photon and gluon polarizations. QCD effective charge is calculated in the finite QCD, exhibiting a clear evidence that the finite QCD is not ruled out but supported by experiment. In the final section, we offer a concise discussion on the softening of anomalies and the treatment of overlapping divergences, accompanied by illustrative examples.