A. L. Kataev

Structure of three-loop contributions to the β-function of N = 1 supersymmetric QED with N f flavors regularized by the dimensional reduction

In the case of using the higher derivative regularization for N = 1 supersymmetric quantum electrodynamics (SQED) with Nf flavors, the loop integrals giving the β-function are integrals of double total derivatives in themomentum space. This feature allows reducing one of the loop integrals to an integral of the δ-function and deriving the Novikov–Shifman–Vainshtein–Zakharov relation for the renormalization group functions defined in terms of the bare coupling constant. We consider N = 1 SQED with Nf flavors regularized by the dimensional reduction in the

The NSVZ scheme for N=1 SQED with Nf flavors, regularized by the dimensional reduction, in the three-loop approximation

\overline {DR}

Analytical five-loop expressions for the renormalization group QED β-function in different renormalization schemes

-scheme. Evaluating the scheme-dependent three-loop contribution to the β-function proportional to (Nf)2 we find the structures analogous to integrals of the δ-singularities. After adding the schemeindependent terms proportional to (Nf)1, we obtain the known result for the three-loop β-function.

Corrections of order \(O(\bar \alpha \bar \alpha _s )\) and \(O(\overline \alpha ^2 )\) to the \(\bar bb\)-decay width of the neutral Higgs boson

At the three-loop level we analyze, how the NSVZ relation appears for 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. INR-TH-2016-033

Infrared renormalons and the relations between the gross-llewellyn smith and the bjorken polarized and unpolarized sum rules

We obtain analytical five-loop results for the renormalization group β-function of Quantum Electrodynamics with the single lepton in different renormalization schemes. The theoretical consequences of the results obtained are discussed.

Analytical singlet α s 4 QCD contributions into the e + e − -annihilation Adler function and the generalized Crewther relations

We present the analytical expressions for the contributions of the order

The improved 10th order QED expression for aμ: new results and related estimates

O(\bar{\alpha}~\bar{\alpha}_s)

Constraints on nonsinglet polarized parton densities from the infrared-renormalon model

and

From perturbative calculations of the QCD static potential towards four-loop pole-running heavy quarks masses relation

O(\bar{\alpha}^2)

The relations between Bjorken polarized, Bjorken unpolarized, and Gross–Llewellyn Smith sum rules

corrections to the decay width of the Standard Model Higgs boson into the