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

Abstract

In this paper we investigate the renormalization of 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 β-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 β-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.

The all-loop perturbative derivation of the NSVZ $$\beta $$-function and the NSVZ scheme in the non-Abelian case by summing singular contributions

“…In the Abelian case this has been proved in all loops [56]. Note that another all-loop NSVZ scheme in the Abelian case is the on-shell scheme [60]. For the renormalization of the photino mass in softly broken N = 1 SQED and for the Adler D-function in N = 1 SQCD the NSVZ-like schemes are also given by the HD+MSL prescription, see Refs.…”

Three-loop contribution of the Faddeev–Popov ghosts to the $$\beta $$-function of $$\mathcal{N}=1$$ supersymmetric gauge theories and the NSVZ relation

“…The rigorous proof of this fact for N = 1 SQED has been done in [48,49]. It also turns out that due to the factorization of the loop integrals into integrals of double total derivatives the NSVZ relation in N = 1 SQED is valid in the on-shell scheme in all loops [50].…”

Two-loop renormalization of the matter superfields and finiteness of $$ \mathcal{N} $$ = 1 supersymmetric gauge theories regularized by higher derivatives

“…The integrals I 6 , I 7 , and I 10 have been calculated in refs. [37,38], and [29], respectively. The results are written as…”

“…In the Abelian case this set has been described in ref. [28] and, in particular, includes the on-shell [29] and HD+MSL [30] schemes. The latter scheme is obtained if a theory is regularized by higher covariant derivatives [31,32] (see refs.…”