NSVZ scheme with the higher derivative regularization for N=1 SQED

TL;DR

This paper demonstrates that the NSVZ relation in N=1 SQED holds exactly when using higher derivative regularization and discusses how to relate different schemes through finite renormalizations, verified by explicit three-loop calculations.

Contribution

It shows that the NSVZ relation is valid in the bare coupling scheme and establishes a method to fix finite renormalizations in the higher derivative regularization approach.

Findings

NSVZ relation holds in the bare coupling scheme.

Finite renormalization can be fixed using higher derivative regularization.

Explicit three-loop calculations verify the scheme relations.

Abstract

The exact NSVZ relation between a $\beta$-function of ${\cal N}=1$ SQED and an anomalous dimension of the matter superfields is studied within the Slavnov higher derivative regularization approach. It is shown that if the renormalization group functions are defined in terms of the bare coupling constant, this relation is always valid. In the renormalized theory the NSVZ relation is obtained in the momentum subtraction scheme supplemented by a special finite renormalization. Unlike the dimensional reduction, the higher derivative regularization allows to fix this finite renormalization. This is made by imposing the conditions $Z_3(\alpha,\mu=\Lambda)=1$ and $Z(\alpha,\mu=\Lambda)=1$ on the renormalization constants of ${\cal N}=1$ SQED, where $\Lambda$ is a parameter in the higher derivative term. The results are verified by the explicit three-loop calculation. In this approximation we relate the $\bar{{DR}}$ scheme and the NSVZ scheme defined within the higher derivative approach by the finite renormalization.