Two-loop renormalization of N=1 supersymmetric electrodynamics, regularized by higher derivatives

TL;DR

This paper calculates the two-loop beta function and anomalous dimension in N=1 supersymmetric QED with higher derivative regularization, finding the beta function to be zero and the anomalous dimension scheme-dependent.

Contribution

It provides explicit two-loop calculations showing the beta function vanishes and discusses scheme dependence of the anomalous dimension in supersymmetric QED.

Findings

Two-loop beta function is zero, independent of regularization form.

Two-loop anomalous dimension can be scheme-independent with a special subtraction scheme.

Results resolve the anomaly puzzle in the context of higher derivative regularization.

Abstract

Two-loop $\beta$-function and anomalous dimension are calculated for N=1 supersymmetric quantum electrodynamics, regularized by higher derivatives in the minimal subtraction scheme. The result for two-loop contribution to the $\beta$-function appears to be equal to 0, does not depend on the form of regularizing term and does not lead to anomaly puzzle. Two-loop anomalous dimension can be also made independent on parameters of higher derivative regularization by a special choice of subtraction scheme.