English

Towards the finite quantum field theory

High Energy Physics - Phenomenology 2025-04-23 v4 High Energy Physics - Theory

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=λ/λ1=\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 λ0\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.

Keywords

Cite

@article{arxiv.2009.07195,
  title  = {Towards the finite quantum field theory},
  author = {Vladimir Sauli},
  journal= {arXiv preprint arXiv:2009.07195},
  year   = {2025}
}

Comments

New two sections on the gauge invariant scheme developed for finite regularization/renormaliztion scheme completes the mission. QCD effective charge was calculated in FRRS. Other Sections, wit exception of the Conclusion has not been touched

R2 v1 2026-06-23T18:33:48.471Z