Two loop divergences studied with one loop Constrained Differential Renormalization

TL;DR

This paper demonstrates how to perform two-loop calculations in gauge theories using one-loop Constrained Differential Renormalization without relying on Ward identities, providing explicit integral lists and beta function coefficients.

Contribution

It introduces a method to compute two-loop divergences directly with one-loop CDR rules, including explicit integral lists and beta function results for several gauge theories.

Findings

Calculated two-loop beta function coefficients for QED, SuperQED, and Yang-Mills.

Provided a list of integrals with overlapping divergences compatible with CDR.

Showed the feasibility of two-loop calculations without Ward identities.

Abstract

In the context of Differential Renormalization, using Constrained Differential Renormalization rules at one loop, we show how to obtain concrete results in two loop calculations without making use of Ward identities. In order to do that, we obtain a list of integrals with overlapping divergences compatible with CDR that can be applied to various two loop background field calculations. As an example, we obtain the two loop coefficient of the beta function of QED, SuperQED and Yang-Mills theory.