Abstract
In this paper we investigate the renormalization of mathcal{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.
Highlights
Among various renormalization schemes that can be used in quantum electrodynamics the subtraction on the mass shell is one of the most important
We have explicitly demonstrated that the NSVZ equation in N = 1 SQED is valid in the on-shell scheme in all orders
In this case it relates the β-function to the mass anomalous dimension
Summary
Among various renormalization schemes that can be used in quantum electrodynamics the subtraction on the mass shell is one of the most important (for a review, see, e.g., [1]). It was discovered that all NSVZ subtraction schemes in N = 1 SQED form a class that can be parameterized by a single function and a single constant [14] Various schemes of this class are related by finite renormalizations satisfying a certain condition, which form a subgroup of the general renormalization group transformations [15,16,17,18]. In this paper we demonstrate that the NSVZ equation relating the β-function to the mass anomalous dimension is valid in the on-shell scheme in all orders. This statement is verified by the explicit calculation.
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