Three-Loop $${\beta}$$-Functions and a Class of the NSVZ Schemes for MSSM Obtained with the Help of the Higher Covariant Derivative Regularization

The three-loop $$\beta$$ -functions and two-loop anomalous dimensions for the MSSM are obtained both in terms of the bare and renormalized couplings in case when the theory is regularized by higher covariant derivatives for an arbitrary supersymmetric subtraction scheme. RGFs defined in terms of the bare couplings satisfy the NSVZ relations in all orders under this regularization. For this reason we start from calculating two-loop anomalous dimensions for all MSSM chiral matter superfields defined in terms of the bare couplings. Using this result, we obtain two-loop anomalous dimensions standardly defined in terms of the renormalized couplings and the three-loop $$\beta$$ -functions defined in terms of the bare couplings from the NSVZ relations. Then the three-loop $$\beta$$ -functions defined in terms of the renormalized couplings are also calculated, and we verify that under certain renormalization prescription they coincide with the $$\overline{\textrm{DR}}$$ -result obtained earlier. Comparing them with the corresponding two-loop anomalous dimensions, we construct a class of renormalization prescriptions for which the NSVZ equations are valid.