NSVZ scheme with the higher derivative regularization for SQED

Abstract

The exact NSVZ relation between a β-function of 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 (α, µ = Λ) = 1 and Z(α, µ = Λ) = 1 on the renormalization constants of N = 1 SQED, where Λ is a parameter in the higher derivative term. The results are verified by the explicit three-loop calculation. In this approximation we relate the DR scheme and the NSVZ scheme defined within the higher derivative approach by the finite renormalization.

Derivation of the exact expression for theDfunction inN=1SQCD

“…In the Abelian case this was proved in all loops [44,45] and confirmed by an explicit threeloop calculations [44,19,32,46]. For a generic non-Abelian gauge theory the factorization of relevant integrals into integrals of double total derivatives was verified only in the two-loop approximation [47,48,49,50,51].…”

“…The difference between the definitions of the RG functions in terms of the bare coupling constant versus renormalized coupling constant is discussed in detail in [19]. In particular, it was demonstrated that the RG functions defined in terms of the bare coupling constant depend on the regularization, but are independent of the subtraction scheme for a fixed regularization.…”

“…In the Abelian case the NSVZ scheme (in which the NSVZ relation is valid in all orders) was constructed in [19] by imposing some simple boundary conditions on the renormalization constants for N = 1 supersymmetric theories regularized by higher derivatives. The higher covariant derivative regularization [35,36] turns out to be very convenient for investigating quantum corrections in supersymmetric theories.…”

One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization

“…The RG functions defined in the standard way in terms of the renormalized coupling constant [37] satisfy the NSVZ relation only in the NSVZ scheme which in this case can be constructed in all orders by imposing simple boundary conditions on the renormalization constants [20,36]. Thus, the NSVZ scheme can be easily constructed with the Slavnov higher derivative regularization.…”

“…It is known [36] that the RG functions defined in terms of the bare couplings depend on the regularization, but do not depend on the subtraction scheme for a fixed regularization.…”