# On-shell renormalization scheme for ${\cal N}=1$ SQED and the NSVZ relation

## TL;DR

This paper demonstrates that the on-shell renormalization scheme in ${
m N}=1$ SQED with higher derivative regularization preserves the exact NSVZ relation at all orders, connecting the beta function and matter superfield anomalous dimension.

## Contribution

It shows that the on-shell scheme is compatible with the NSVZ relation and fits into the continuous set of NSVZ subtraction schemes, with explicit two- and three-loop calculations.

## Key findings

- NSVZ relation holds in the on-shell scheme at all orders
- Explicit two- and three-loop calculations confirm scheme compatibility
- Finite renormalizations relate on-shell scheme to other NSVZ schemes

## Abstract

In this paper we investigate the renormalization of ${\cal N}=1$ supersymmetric quantum electrodynamics, regularized by higher derivatives, in the on-shell scheme. It is demonstrated that in this scheme the exact Novikov, Shifman, Vainshtein, and Zakharov (NSVZ) equation relating the $\beta$-function to the anomalous dimension of the matter superfields is valid in all orders of the perturbation theory. This implies that the on-shell scheme enters the recently constructed continuous set of NSVZ subtraction schemes. To verify this statement, we compare the anomalous dimension of the matter superfields in the two-loop approximation and the $\beta$-function in the three-loop approximation, which are explicitly calculated in this scheme. The finite renormalizations relating the on-shell scheme to some other NSVZ subtraction schemes formulated previously are obtained.