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Three-loop $\beta$-functions of the Minimal Supersymmetric Standard Modelregularized by higher covariant derivatives are obtained for an arbitrarysupersymmetric subtraction scheme. For this purpose we first calculate two-loopanomalous dimensions for all MSSM chiral matter superfields defined in terms ofthe bare couplings. Then we use the NSVZ equations for the renormalizationgroup functions defined in terms of the bare couplings, which are valid in allorders in the case of using the higher covariant derivative regularization.This gives the three-loop $\beta$-functions defined in terms of the barecouplings. After that, we construct the three-loop $\beta$-functions and thetwo-loop anomalous dimensions standardly defined in terms of the renormalizedcouplings for an arbitrary subtraction scheme. As a nontrivial correctnesstest, we verify that for a certain renormalization prescription the generalresults 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.

the journal of high energy physics/the journal of high energy physics

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