One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization

TL;DR

This paper calculates one-loop divergences in non-Abelian supersymmetric gauge theories regularized with a BRST-invariant higher derivative method, confirming known beta-function results and showing ghost vertex non-renormalization.

Contribution

It demonstrates that the one-loop beta-function integrals are double total derivatives regardless of the higher derivative choice, confirming the robustness of the regularization method.

Findings

Reproduces the known one-loop beta-function result.

Shows that certain ghost vertices are not renormalized at one loop.

Confirms the double total derivative structure of the integrals.

Abstract

We consider a general non-Abelian renormalizable ${\cal N}=1$ supersymmetric gauge theory, regularized by higher covariant derivatives without breaking the BRST invariance, and calculate one-loop divergences for a general form of higher derivative regulator and of the gauge fixing term. It is demonstrated that the momentum integrals giving the one-loop $\beta$-function are integrals of double total derivatives independently of a particular choice of the higher derivative term. Evaluating them we reproduce the well-known result for the one-loop $\beta$-function. Also we find that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in the considered approximation.