arXiv subjects

S. S. Aleshin

Publications and source records attributed to S. S. Aleshin.

8 recordsLinked to original sources

arXiv2020

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

We verify a recently proposed method for obtaining a $β$-function of ${\cal N}=1$ supersymmetric gauge theories regularized by higher derivatives by an explicit calculation. According to this method, a $β$-function can be found by calculating specially modified vacuum supergraphs instead of a much larger number of the two-point superdiagrams. The result is produced in the form of a certain integral of double total derivatives with respect to the loop momenta. Here we compare the results obtained for the three-loop $β$-function of ${\cal N}=1$ SQED in the general $ξ$-gauge with the help of this method and with the help of the standard calculation. Their coincidence confirms the correctness of the new method and the general argumentation used for its derivation. Also we verify that in the considered approximation the NSVZ relation is valid for the renormalization group functions defined in terms of the bare coupling constant and for the ones defined in terms of the renormalized coupling constant in the HD+MSL scheme, both its sides being gauge-independent.

hep-th↗

arXiv2020

The three-loop Adler $D$-function for ${\cal N}=1$ SQCD with various renormalization prescriptions

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 matter superfields. However this NSVZ-like equation can be restored by a special tuning of the renormalization scheme. Also we demonstrate that the $D$-function defined in terms of the bare coupling does not satisfy the NSVZ-like equation in the case of using the regularization by dimensional reduction. The scheme-dependence of the $D$-function written in the form of the $β$-expansion is briefly discussed.

hep-th↗

arXiv2019

The three-loop Adler $D$-function for ${\cal N}=1$ SQCD regularized by dimensional reduction

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 theory regularized by higher derivatives we find a subtraction scheme in which the Green functions coincide with the ones obtained with the dimensional reduction and the modified minimal subtraction prescription for the renormalization of the SQCD coupling constant and of the matter superfields. Also we calculate the $D$-function in the $\overline{\mbox{DR}}$ scheme for all renormalization constants (including the one for the electromagnetic coupling constant which appears due to the SQCD corrections). It is shown that the results do not satisfy the NSVZ-like equation relating the $D$-function to the anomalous dimension of the matter superfields. However, the NSVZ-like scheme can be constructed with the help of a properly tuned finite renormalization. It is also demonstrated that the three-loop $D$-function defined in terms of the bare couplings with the dimensional reduction does not satisfy the NSVZ-like equation for an arbitrary renormalization prescription. We also investigate a possibility to present the results in the form of the $β$-expansion and the scheme dependence of this expansion.

hep-th↗

arXiv2017

NSVZ relation and the dimensional reduction in ${\cal N}=1$ SQED

It is known that factorization of the $β$-function loop integrals into integrals of double total derivatives is an important ingredient needed for deriving the NSVZ relation by direct perturbative calculations in ${\cal N}=1$ SQED regularized by the higher derivatives. It allows to relate the $β$-function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant. In this work we find the analog of this result in the case of using dimensional reduction regularization in the lowest orders. However, we demonstrate that in this case the NSVZ relation is not satisfied for the RG functions defined in terms of the bare coupling constant. Nevertheless, it is possible to impose boundary conditions to the renormalization constants determining the NSVZ scheme in the three-loop order for the RG functions defined in terms of the renormalized coupling constant.

hep-th↗

arXiv2016

The NSVZ scheme for ${\cal N}=1$ SQED with $N_f$ flavors, regularized by the dimensional reduction, in the three-loop approximation

At the three-loop level we analyze, how the NSVZ relation appears for ${\cal N}=1$ SQED regularized by the dimensional reduction. This is done by the method analogous to the one which was earlier used for the theories regularized by higher derivatives. Within the dimensional technique, the loop integrals cannot be written as integrals of double total derivatives. However, similar structures can be written in the considered approximation and are taken as a starting point. Then we demonstrate that, unlike the higher derivative regularization, the NSVZ relation is not valid for the renormalization group functions defined in terms of the bare coupling constant. However, for the renormalization group functions defined in terms of the renormalized coupling constant, it is possible to impose boundary conditions to the renormalization constants giving the NSVZ scheme in the three-loop order. They are similar to the all-loop ones defining the NSVZ scheme obtained with the higher derivative regularization, but are more complicated. The NSVZ schemes constructed with the dimensional reduction and with the higher derivative regularization are related by a finite renormalization in the considered approximation.

hep-th↗

arXiv2016

One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization

We consider a general non-Abelian renormalizable ${\cal N}=1$ supersymmetric gauge theory, regularized by higher covariant derivatives without breaking the BRST invariance, and calculate one-loop divergences for a general form of higher derivative regulator and of the gauge fixing term. It is demonstrated that the momentum integrals giving the one-loop $β$-function are integrals of double total derivatives independently of a particular choice of the higher derivative term. Evaluating them we reproduce the well-known result for the one-loop $β$-function. Also we find that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in the considered approximation.

hep-th↗

arXiv2015

Structure of three-loop contributions to the beta-function of N=1 SQED with N_f flavors, regularized by the dimensional reduction

In the case of using the higher derivative regularization for $N=1$ SQED with $N_f$ flavors the loop integrals giving the $β$-function are integrals of double total derivatives in the momentum space. This feature allows to reduce one of the loop integrals to an integral of the $δ$-function and to derive the NSVZ relation for the renormalization group functions defined in terms of the bare coupling constant. In this paper we consider $N=1$ SQED with $N_f$ flavors regularized by the dimensional reduction in the $\overline{\mbox{DR}}$-scheme. Evaluating the scheme-dependent three-loop contribution to the $β$-function proportional to $(N_f)^2$ we find the structures analogous to integrals of the $δ$-singularities. After adding the scheme-independent terms proportional to $(N_f)^1$ we obtain the known result for the three-loop $β$-function.

hep-th↗

arXiv2013

Does the Borexino experiment have enough resolution to detect the neutrino flavor day-night asymmetry?

The Earth's density distribution can be approximately considered piecewise continuous at the scale of two-flavor oscillations of neutrinos with energies about 1 MeV. This quite general assumption appears to be enough to analytically calculate the day-night asymmetry factor. Using the explicit time averaging procedure, we show that, within the leading-order approximation, this factor is determined by the electron density immediately before the detector, i.e. in the Earth's crust. Within the approximation chosen, the resulting asymmetry factor does not depend either on the properties of the inner Earth's layers or on the substance and the dimensions of the detector. For beryllium neutrinos, we arrive at the asymmetry factor estimation of about $-4 \times 10^{-4}$, which is at least one order of magnitude beyond the present experimental resolution, including that of the Borexino experiment.

hep-ph↗