The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD with various renormalization prescriptions

Abstract

The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD in the $\overline{\mbox{DR}}$ scheme is calculated. It appears that the result does not satisfy NSVZ-like equation which relates the $D$-function to the anomalous dimension of the matter superfields. However this NSVZ-like equation can be restored by a special tuning of the renormalization scheme. Also we demonstrate that the $D$-function defined in terms of the bare coupling does not satisfy the NSVZ-like equation in the case of using the regularization by dimensional reduction. The scheme-dependence of the $D$-function written in the form of the $\beta$-expansion is briefly discussed.

4 pages, submitted to the Proceedings of 19th Lomonosov Conference on Elementary Particle Physics (Moscow State University, August 22-28, 2019)