The NSVZ scheme forN=1SQED with N f flavors, regularized by the dimensional reduction, in the three-loop approximation

Abstract

At the three-loop level we analyze, how the NSVZ relation appears for N = 1 SQED regularized by the dimensional reduction. This is done by the method analogous to the one which was earlier used for the theories regularized by higher derivatives. Within the dimensional technique, the loop integrals cannot be written as integrals of double total derivatives. However, similar structures can be written in the considered approximation and are taken as a starting point. Then we demonstrate that, unlike the higher derivative regularization, the NSVZ relation is not valid for the renormalization group functions defined in terms of the bare coupling constant. However, for the renormalization group functions defined in terms of the renormalized coupling constant, it is possible to impose boundary conditions to the renormalization constants giving the NSVZ scheme in the three-loop order. They are similar to the all-loop ones defining the NSVZ scheme obtained with the higher derivative regularization, but are more complicated. The NSVZ schemes constructed with the dimensional reduction and with the higher derivative regularization are related by a finite renormalization in the considered approximation.

New form of the exact NSVZ β-function: the three-loop verification for terms containing Yukawa couplings

“…The former RGFs are independent of the renormalization prescription, but depend on the regularization. It is possible to demonstrate that with dimensional reduction they do not satisfy the NSVZ equation, see [35,36]. However, if an N = 1 supersymmetric gauge theory is regularized by higher derivatives, then, at least in the Abelian case, the NSVZ relation is valid for RGFs defined in terms of the bare coupling constants independently of the subtraction scheme [37,38].…”

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

“…[14], which also includes the all-order HD+MSL prescription and the NSVZ scheme constructed with dimensional reduction in the three-loop approximation in Refs. [39,43]. According to Ref.…”

“…The difference between calculations with the higher derivative regularization and with dimensional reduction for N = 1 SQED in the three-loop approximation has been analyzed in Ref. [43].…”

NSVZ-like scheme for the photino mass in softly broken N = 1 SQED regularized by higher derivatives

“…In the case of using the dimensional reduction[33] this limit is not well-defined. Therefore, the factorization into double total derivatives does not take place in this case[34], and the RG functions defined in terms of the bare coupling constant do not satisfy the NSVZ relation[35] 3. General equations which describe, how the NSVZ relation is changed under the finite renormalizations are presented in Refs [41,42,43]…”