A class of the NSVZ renormalization schemes for ${\cal N}=1$ SQED

TL;DR

This paper explores a class of renormalization schemes in ${ m ext{N}}=1$ SQED where the NSVZ relation between the beta function and anomalous dimension holds at all loops, revealing an infinite set of such schemes connected by finite renormalizations.

Contribution

The paper identifies an infinite family of renormalization schemes preserving the NSVZ relation in ${ m ext{N}}=1$ SQED and characterizes their structure and parameterization.

Findings

Existence of an infinite set of NSVZ-preserving schemes.

Finite renormalizations form a group parameterized by a function and a constant.

Explicit three-loop calculations confirm the theoretical results.

Abstract

For the ${\cal N}=1$ supersymmetric electrodynamics we investigate renormalization schemes in which the NSVZ equation relating the $\beta$-function to the anomalous dimension of the matter superfields is valid in all loops. We demonstrate that there is an infinite set of such schemes. They are related by finite renormalizations which form a group and are parameterized by one finite function and one arbitrary constant. This implies that the NSVZ $\beta$-function remains unbroken if the finite renormalization of the coupling constant is related to the finite renormalization of the matter superfields by a special equation derived in this paper. The arbitrary constant corresponds to the arbitrariness of choosing the renormalization point. The results are illustrated by explicit calculations in the three-loop approximation.