The all-loop perturbative derivation of the NSVZ $$\beta $$-function and the NSVZ scheme in the non-Abelian case by summing singular contributions

et al. 2021

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We investigate the NSVZ relations for $$ \mathcal{N} $$ N = 1 supersymmetric gauge theories with multiple gauge couplings. As examples, we consider MSSM and the flipped SU(5) model, for which they easily reproduce the results for the two-loop β-functions. For $$ \mathcal{N} $$ N = 1 SQCD interacting with the Abelian gauge superfield we demonstrate that the NSVZ-like equation for the Adler D-function follows from the NSVZ relations. Also we derive all-loop equations describing how the NSVZ equations for theories with multiple gauge couplings change under finite renormalizations. They allow describing a continuous set of NSVZ schemes in which the exact NSVZ β-functions are valid for all gauge coupling constants. Very likely, this class includes the HD+MSL scheme, which is obtained if a theory is regularized by Higher covariant Derivatives and divergences are removed by Minimal Subtractions of Logarithms. That is why we also discuss how one can construct the higher derivative regularization for theories with multiple gauge couplings. Presumably, this regularization allows to derive the NSVZ equations for such theories in all loops. In this paper we make the first step of this derivation, namely, the NSVZ equations for theories with multiple gauge couplings are rewritten in a new form which relates the β-functions to the anomalous dimensions of the quantum gauge superfields, of the Faddeev-Popov ghosts, and of the matter superfields. The equivalence of this new form to the original NSVZ relations follows from the extension of the non-renormalization theorem for the triple gauge-ghost vertices, which is also derived in this paper.

Section: Jhep10(2021)046mentioning

confidence: 99%

“…The all-loop proof that the HD+MSL prescription gives some NSVZ schemes [63] is based on the all-loop derivation of the NSVZ equation in refs. [63][64][65], see also ref. [66].…”

Section: Jhep10(2021)046mentioning

confidence: 99%

“…The sum of these singularities has been calculated in [63]. (The sums of ghost and matter singularities have also been calculated by a different method in ref.…”

Section: Jhep10(2021)046mentioning

confidence: 99%

Section: General Features Of the Higher Derivative Regularization In Supersymmetric Theories With Multiple Gauge Couplingsmentioning

confidence: 99%

Section: Jhep10(2021)046mentioning

confidence: 99%

See 3 more Smart Citations

The NSVZ relations for $$ \mathcal{N} $$ = 1 supersymmetric theories with multiple gauge couplings

Korneev

Плотников

et al. 2021

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The three-loop anomalous dimension and the four-loop β-function for $$ \mathcal{N} $$ = 1 SQED regularized by higher derivatives

Shirokov

2022

For $$ \mathcal{N} $$ N = 1 SQED with Nf flavors regularized by higher derivatives in the general ξ-gauge we calculate the three-loop anomalous dimension of the matter superfields defined in terms of the bare coupling constant and demonstrate its gauge independence. After this the four-loop β-function defined in terms of the bare coupling constant is obtained with the help of the NSVZ equation, which is valid for these renormalization group functions in all loops. Next, we calculate the three-loop anomalous dimension and the four-loop β-function defined in terms of the renormalized coupling constant for an arbitrary subtraction scheme supplementing the higher derivative regularization. Then we construct a renormalization prescription for which the results coincide with the ones in the $$ \overline{\mathrm{DR}} $$ DR ¯ -scheme and describe all NSVZ schemes in the considered approximation. Also we demonstrate the existence of a subtraction scheme in which the anomalous dimension does not depend on Nf, while the β-function contains only terms of the first order in Nf. This scheme is obtained with the help of a finite renormalization compatible with a structure of quantum corrections and is NSVZ. The existence of such an NSVZ scheme is also proved in all loops.

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

Haneychuk

Shirokova

2022

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Three-loop β-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 β-functions defined in terms of the bare couplings. After that, we construct the three-loop β-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 $$ \overline{\mathrm{DR}} $$ DR ¯ scheme. Also this can be considered as an indepedent confirmation of the $$ \overline{\mathrm{DR}} $$ DR ¯ results.