Related papers: NSVZ scheme with the higher derivative regularizat…
The contributions of the matter superfields and of the Faddeev--Popov ghosts to the $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories defined in terms of the bare couplings are calculated in all orders in the case of using the…
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…
We consider the softly broken ${\cal N}=1$ supersymmetric electrodynamics, regularized by higher derivatives. For this theory we demonstrate that the renormalization of the photino mass is determined by integrals of double total derivatives…
Recently the exact NSVZ $\beta$-function was rewritten in the form of a relation between the $\beta$-function and the anomalous dimensions of the quantum gauge superfield, of the Faddeev--Popov ghosts, and of the matter superfields. It was…
We calculate the Adler $D$-function for ${\cal N}=1$ SQCD in the three-loop approximation using the higher covariant derivative regularization and the NSVZ-like subtraction scheme. The recently formulated all-order relation between the…
For N=1 supersymmetric quantum electrodynamics, regularized by higher derivatives, a method for summation of all Feynman diagrams defining the beta-function is presented. Using this method we prove that the beta-function is given by an…
In the case of using the higher derivative regularization for $N=1$ SQED with $N_f$ flavors the loop integrals giving the $\beta$-function are integrals of double total derivatives in the momentum space. This feature allows to reduce one of…
Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not…
We explore the relationship between the DRED and NSVZ schemes. Using certain exact results for the soft scalar mass $\beta$-function, we derive the transformation of $\alpha^{\DRED}$ to $\alpha^{\NSVZ}$ through terms of order $\alpha^4$. We…
For renormalizable theories with a single coupling constant regularized by higher derivatives we investigate the coefficients at powers of logarithms present in the renormalization constants assuming that divergences are removed by minimal…
Some recent research of quantum corrections in ${\cal N}=1$ supersymmetric theories is briefly reviewed. The most attention is paid to the theories regularized by higher covariant derivatives. In particular, we discuss, how the NSVZ and…
Using the Slavnov--Taylor identities we prove that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in all loops in ${\cal N}=1$ supersymmetric gauge theories. This statement is verified…
There have been known "exact" beta functions for the gauge coupling in N=1 supersymmetric gauge theories, the so-called NSVZ beta functions. Shifman and Vainshtein (SV) further related these beta functions to the exact 1-loop running of the…
The three-loop Adler $D$-function for ${\cal N}=1$ SQCD in the $\overline{\mbox{DR}}$ scheme is calculated starting from the three-loop result recently obtained with the higher covariant derivative regularization. For this purpose, for the…
We investigate the connection between the NSVZ and the DRED forms of the gauge $\beta$-function in an $N=1$ supersymmetric gauge theory. We construct a coupling constant redefinition that relates the two forms up to four loops. By abelian…
We find the three-loop contribution to the $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives produced by the supergraphs containing loops of the Faddeev--Popov ghosts. This is done…
The NSVZ $\beta$ functions in two-dimensional $\mathcal N=(0,2)$ supersymmetric models are revisited. We construct and discuss a broad class of such models using the gauge formulation. All of them represent direct analogs of…
The three-loop Adler $D$-function for ${\cal N}=1$ 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…
For $\mathcal{N}=1$ supersymmetric Yang-Mills theory without matter it is demonstrated that there is a class of renormalization schemes, in which the exact Novikov, Shifman, Vainshtein, and Zakharov (NSVZ) formula for the renormalization…
We consider an ${\cal N}=1$ nonrenormalizable supersymmetric gauge theory with the superpotential quartic in the chiral matter superfields. With the help of the Slavnov's higher covariant derivative regularization it is demonstrated that…