Three-loop $\beta$-functions and two-loop anomalous dimensions for MSSM regularized by higher covariant derivatives in an arbitrary supersymmetric subtraction scheme

TL;DR

This paper derives three-loop beta functions and two-loop anomalous dimensions for the MSSM using higher covariant derivative regularization, applicable to any subtraction scheme, and confirms consistency with known results in the R scheme.

Contribution

It provides the first three-loop beta functions for MSSM with higher covariant derivatives in a general subtraction scheme, extending previous two-loop anomalous dimension calculations.

Findings

Derived three-loop Fs for MSSM with higher covariant derivatives.

Confirmed consistency with R scheme results.

Validated the approach with known special cases.

Abstract

Three-loop $\beta$-functions of the Minimal Supersymmetric Standard Model regularized by higher covariant derivatives are obtained for an arbitrary supersymmetric subtraction scheme. For this purpose we first calculate two-loop anomalous dimensions for all MSSM chiral matter superfields defined in terms of the bare couplings. Then we use the NSVZ equations for the renormalization group functions defined in terms of the bare couplings, which are valid in all orders in the case of using the higher covariant derivative regularization. This gives the three-loop $\beta$-functions defined in terms of the bare couplings. After that, we construct the three-loop $\beta$-functions and the two-loop anomalous dimensions standardly defined in terms of the renormalized couplings for an arbitrary subtraction scheme. As a nontrivial correctness test, we verify that for a certain renormalization prescription the general results reproduce the ones obtained earlier in the $\overline{\mbox{DR}}$ scheme. Also this can be considered as an indepedent confirmation of the $\overline{\mbox{DR}}$ results.