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We verify a recently proposed method for obtaining a $\beta$-function of${\cal N}=1$ supersymmetric gauge theories regularized by higher derivatives byan explicit calculation. According to this method, a $\beta$-function can befound by calculating specially modified vacuum supergraphs instead of a muchlarger number of the two-point superdiagrams. The result is produced in theform of a certain integral of double total derivatives with respect to the loopmomenta. Here we compare the results obtained for the three-loop$\beta$-function of ${\cal N}=1$ SQED in the general $\xi$-gauge with the helpof this method and with the help of the standard calculation. Their coincidenceconfirms the correctness of the new method and the general argumentation usedfor its derivation. Also we verify that in the considered approximation theNSVZ relation is valid for the renormalization group functions defined in termsof the bare coupling constant and for the ones defined in terms of therenormalized coupling constant in the HD+MSL scheme, both its sides beinggauge-independent.

nuclear physics b

Three-loop verification of a new algorithm for the calculation of a  $\beta$-function in supersymmetric theories regularized by higher derivatives  for the case of ${\cal N}=1$ SQED