Relation between leading divergences in nonrenormalizable $4D$ supersymmetric theories

Abstract

We consider an ${\cal N}=1$ nonrenormalizable supersymmetric gauge theory with the superpotential quartic in the chiral matter superfields. With the help of the Slavnov's higher covariant derivative regularization it is demonstrated that (in the lowest nontrivial order) the leading power divergent quantum correction to the gauge coupling constant is given by an integral of double total derivatives with respect to the loop momenta. The result obtained after calculating this integral turned out to be proportional to the corresponding quantum correction to the kinetic term of the matter superfields. More exactly, in the considered approximation the quadratically divergent contributions to the gauge coupling and to the kinetic term of the chiral matter superfields are related by an equation analogous to the exact NSVZ $\beta$-function for the renormalizable case.