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We consider heavy quark contributions to the polarized Bjorken sum rule. We found good agreement between the experimental data and the predictions of analytic QCD. To satisfy the limit of photoproduction, we use new representation of the perturbative part of the polarized Bjorken sum rule, proposed recently., Comment: 11 pages, 4 figures

We present the results of [1], where good agreement was obtained between calculations within the framework of analytic QCD and experimental data on polarized Bjorken sum rule. The photoproduction limit was also considered and a new representation of the perturbative contribution to the polarized Bjorken sum rule was obtained., Comment: 10 pages, 2 figures, contribution to the proceedings of Scientific session of Nuclear Physics section of Physics Division of RAS "Physics of Fundamental Interactions" (April 1-5, Dubna, Russia)

Anomalous dimension of the shortest single-trace operator is calculated in a simple form for the fishnet limit of the twisted ABJM model in 3D., Comment: 14 pages, 2 figures

Nuclear deep inelastic structure functions F_2^A(x,Q^2) as well as parton distribution functions in a nuclei are investigated in the framework of rescaling model. Our analysis is based on analytical expressions for quark and gluon densities in a proton derived at the leading order of QCD coupling. By fitting the rescaling parameters from the experimental data on F_2^A(x,Q^2)/F_2^D(x,Q^2) ratio for several nuclear targets, we derive predictions for corresponding nuclear parton distributions and, thus, for shadowing and antishadowing effects., Comment: 9 pages, 2 figures

We found good agreement between the experimental data obtained for the polarized Bjorken sum rule and the predictions of analytic QCD, as well as a strong difference between these data and the results obtained in the framework of perturbative QCD. To satisfy the limit of photoproduction and take into account Gerasimov-Drell-Hearn and Burkhardt-Cottingham sum rules, we develope new representation of the perturbative part of the polarized Bjorken sum rule., Comment: 17 pages, 6 figures

The deep inelastic scattering data on the nucleon F_2 structure function, accumulated by BCDMS, SLAC and NMC collaborations in fixed-target experiments, are analyzed in the non-singlet approximation within the frameworks of both conventional \overline{\mathbf{MS}} scheme as well as those with resummations of logarithms at large Bjorken x values. The use of the latter is important because they greatly modify the values of the twist four corrections while leaving a strong coupling constant almost intact., Comment: 15 pages, 1 figure

Analytical expressions for the Transverse Momentum Dependent (TMD, or unintegrated) gluon and sea quark densities in nuclei are derived at leading order of QCD running coupling. The calculations are performed in the framework of the rescaling model and Kimber-Martin-Ryskin (KMR) prescription, where the Bessel-inspired behavior of parton densities at small Bjorken $x$ values, obtained in the case of flat initial conditions in the double scaling QCD approximation, is applied. The derived expressions are used to evaluate the inclusive heavy flavor production in proton-lead collisions at the LHC. We find a good agreement of our results with latest experimental data collected by the CMS and ALICE Collaborations at $\sqrt s = 5.02$ GeV., Comment: 13 pages, 3 figures, 1 table

We present a brief overview of fractional analytic QCD., Comment: 7 pages, 1 figure, contribution to the proceedings of the XXVth International Baldin Seminar on High Energy Physics Problems Relativistic Nuclear Physics and Quantum Chromodynamics (September 18-23, Dubna, Russia)

The low-x behavior of the linearly polarized gluon density h_{g}(x,k_t^2, Q^2) in nuclei is studied in the rescaling model at small transverse momentum k_t., Comment: 7 pages, 1 figure

Based on a solution of DGLAP evolution equations at small values of Bjorken variable x, a simple analytic approximation for so-called linearly polarized gluon density \tilde{h}_1^{\perp g}(x,k_t^2, Q^2) is obtained at LO of perturbation theory., Comment: 6 pages, 4 figures

A brief review of the results for the total cross section \sigma^{\nu N} of ultrahigh-energy neutrino deep inelastic scattering on isoscalar nuclear targets is presented. These results are based on simple approximations for \sigma^{\nu N} and are compared with the experimental data of the IceCube Collaboration. The total cross section \sigma^{\nu N} is proportional to the structure function F_2^{\nu N}(M_V^2/s,M_V^2), where M_V is the intermediate boson mass and s is square of the energy of the center of mass. The coefficient in the front of F_2^{\nu N}(M_V^2/s,M_V^2) depends on the asymptotic behavior of F_2^{\nu N} at low values of x. It contains an additional term \sim \ln{s} if F_2^{\nu N} is scaled by the power \ln(1/x). Therefore, the asymptotic behavior of F_2^{\nu N}\propto\ln^2(1/x) for small x often assumed in the literature already leads to violation of the Froissart bound for \sigma^{\nu N}., Comment: 10 pages, 1 figure, contribution to the proceedings of the 4th International Symposium on Cosmic Rays and Astrophysics (June 27-29, Moscow, Russia)

The experimental data obtained for the polarized Bjorken sum rule \Gamma^{(p-n)}_1(Q^2) for small values of Q2 are approximated by the predictions obtained in the framework of analytic QCD up to the 5th order perturbation theory, whose coupling constant does not contain the Landau pole. We found an excellent agreement between the experimental data and the predictions of analytic QCD, as well as a strong difference between these data and the results obtained in the framework of standard QCD., Comment: 9 pages, 1 figure

We present the results of studies [1,2] of the gauge covariance of the massless fermion propagator in three-dimensional quenched quantum electrodynamics in the framework of dimensional regularization in d=3-2\ep. Assuming the finiteness of the perturbative expansion, i.e. existence of the limit \ep \to 0, it was shown in [1] that exactly for d=3 all odd perturbative coefficients, starting from the third order, must be equal to zero in any gauge. To test this, in Ref. [2] we calculated three- and four-loop corrections to the massless fermionic propagator. Three-loop corrections are finite and gauge-invariant, while four-loop corrections have singularities. The terms depending on the gauge parameter are completely determined by the lower orders in accordance with the Landau-Khalatnikov-Fradkin transformation., Comment: 12 pages, contribution to the proceedings of VII International Conference "Models in Quantum Field Theory" (October 10-14, Saint Petersburg, Russia)

We review field theoretical studies dedicated to understanding the effects of electron-electron interaction in graphene, which is characterized by gapless bands, strong electron-electron interactions, and emerging Lorentz invariance deep in the infrared. We consider the influence of interactions on the transport properties of the system as well as their supposedly decisive influence on the potential dynamical generation of a gap., Comment: 5 pages, contribution to the proceedings of International Conference "Modern problems of condensed matter theory" (October 17-22, Dubna, Russia)

We present a brief overview of fractional analytic QCD, basically following the results recently obtained in Refs. [1,2]., Comment: 8 pages, 2 figures, contribution to the proceedings of the XXIV International Seminar on High Energy Physics "From quarks to galaxies: clearing up the dark sides" (November 22-24, Protvino, Russia)

In this paper we show that, as in the spacelike case, the inverse logarithmic expansion is applicable for all values of the argument of the analytic coupling constant. We present two different approaches, one of which is based primarily on trigonometric functions, and the latter is based on dispersion integrals. The results obtained up to the 5th order of perturbation theory, have a compact form and their acquiring is much easier than the methods that have been used before. As an example, we apply our results to study the Higgs boson decay into a bb pair., Comment: 30 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:2203.09307

We give predictions for the ratio RQ(x,Q2)=FLQ(x,Q2)/F2Q(x,Q2) at small values of Bjorken variable x in the first three orders of perturbation theory. We show an approximate x-independence of RQ(x,Q2) at low x and non-large Q2 values (Q2 < 8--10 m2Q), irrespectively on the gluon density in a proton used in the calculations. This observation could be useful in subsequent phenomenological studies of the heavy flavor production at future lepton-hadron and hadron-hadron colliders., Comment: 10 pages, 3 figures

The behavior of the gluon density in nuclei is investigated in the framework of the rescaling model., Comment: 6 pages, 1 figure

The main steps of the process of obtaining the result [1] in terms of elliptic polylogarithms for a two-loop sunrise integral with two different internal masses with pseudothreshold kinematics for all orders of the dimensional regulator are shown., Comment: 7 pages, contribution to the proceedings of the International Conference on Quantum Field Theory, High-Energy Physics, and Cosmology (July 18 - 21, 2022; Dubna, Russia)

A new type of parametrization for parton distribution functions in a proton, based on their $Q^2$-evolution at large and small $x$ values, is constructed. In our analysis, the valence and nonsinglet parts obey the Gross-Llewellyn-Smith and Gottfried sum rules, respectively. For the singlet quark and gluon densities momentum conservation is taken into account. Then, using the Kimber-Martin-Ryskin prescription, we extend the consideration to Transverse Momentum Dependent (TMD, or unintegrated) gluon and quark distributions in a proton, which currently plays an important role in a number of phenomenological applications. The analytical expressions for the latter, valid for both low and large $x$, are derived for the first time., Comment: 28 pages, 8 figures

We present an overview of fractional analytic QCD beyond leading order, following the results recently obtained in Ref. [1]. We demonstrate four different representations, the details of their derivation, and show the applicability of analytic QCD to the analysis of the Bjorken sum rule., Comment: 25 pages, 14 figures, contribution to the proceedings of the International Workshop on Elementary Particles and Nuclear Physics (April 24-30, Almaty, Kazakhstan)

We consider new ways of obtaining series and integral representations for master integrals arising in the process of matching of QCD to NRQCD. The latter results are exact in space-time dimension $d$. In addition, we discuss series expansion of the obtained results at fixed values of $d$., Comment: 15 pages, 1 figure

Fractional analytic QCD is constructed beyond leading order using the standard inverse logarithmic expansion. It is shown that, contrary to the usual QCD coupling constant, for which this expansion can be used only for large values of its argument, in the case of analytic QCD, the inverse logarithmic expansion is applicable for all values of the argument of the analytic coupling constant. We present four different views, two of which are based primarily on Polylogarithms and generalized Euler $\zeta$-functions, and the other two are based on dispersion integrals. The results obtained up to the 5th order of perturbation theory, have a compact form and do not contain complex special functions that were used to solve this problem earlier. As an example, we apply our results to study the polarized Bjorken sum rule, which is currently measured very accurately., Comment: 39 pages, 16 figures

This document provides a comprehensive summary of the state-of-the-art, challenges, and prospects in the experimental and theoretical study of the strong coupling $\alpha_s$. The current status of the seven methods presently used to determine $\alpha_s$ based on: (i) lattice QCD, (ii) hadronic $\tau$ decays, (iii) deep-inelastic scattering and parton distribution functions fits, (iv) electroweak boson decays, hadronic final-states in (v) e+e-, (vi) e-p, and (vii) p-p collisions, and (viii) quarkonia decays and masses, are reviewed. Novel $\alpha_s$ determinations are discussed, as well as the averaging method used to obtain the PDG world-average value at the reference Z boson mass scale, $\alpha_s(m^2_Z)$. Each of the extraction methods proposed provides a "wish list" of experimental and theoretical developments required in order to achieve an ideal permille precision on $\alpha_s(m^2_Z)$ within the next 10 years., Comment: 130 pages, 82 figures. White paper submitted to the Energy Frontier "Proceedings of the US Community Study on the Future of Particle Physics" (Snowmass 2021)

Deep inelastic scattering data on $F_2$ structure function from various fixed-target experiments were analyzed in a nonsinglet approximation in the MSbar and DIS scheme. The study of high statistics deep inelastic scattering data provided by BCDMS, SLAC and NMC collaborations, was carried out using a combined analysis. The application of the DIS scheme leads to the resummation of contributions that are important for large x values. It is found that using the DIS scheme does not significantly change the strong coupling constant itself but does strongly change the values of the twist-four corrections., Comment: 7 pages

We show some examples of calculations of massless and massive Feynman integrals., Comment: 22 pages. arXiv admin note: text overlap with arXiv:2004.06625

To study the heavy quark production processes, we use the transverse momentum dependent (TMD, or unintegrated) gluon distribution function in a proton obtained recently using the Kimber-Martin-Ryskin prescription from the Bessel-inspired behavior of parton densities at small Bjorken $x$ values. We obtained a good agreement of our results with the latest HERA experimental data for reduced cross sections $\sigma^{c\overline{c}}_{\rm red}(x,Q^2)$ and $\sigma^{b\overline{b}}_{\rm red}(x,Q^2)$, and also for deep inelastic structure functions $F_2^c(x,Q^2)$ and $F_2^b(x,Q^2)$ in a wide range of $x$ and $Q^2$ values. Comparisons with the predictions based on the Ciafaloni-Catani-Fiorani-Marchesini evolution equation and with the results of conventional pQCD calculations performed at first three orders of perturbative expansion are presented., Comment: 28 pages, 5 figures

The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion coefficients are shown, and modern methods based on differential equations are considered., Comment: 22 pages; contribution to the proceedings of the International Conference "Antidifferentiation and the Calculation of Feynman Amplitudes" (4-9 October 2020, Zeuthen, Germany). arXiv admin note: text overlap with arXiv:2004.06625

An exact formula that relates standard zeta functions and so-called hatted zeta functions in all orders of perturbation theory is presented. This formula is based on the Landau-Khalatnikov-Fradkin transformation, Comment: 5 pages; contribution to the proceedings of the Session-Conference of Nuclear Physics Section at the Department of Physical Sciences, Russian Academy of Sciences (March 10-12, 2020; Novosibirsk, Russia); based on arXiv:1906.10930 and arXiv:1912.10957

We calculate the three- and four-loop corrections to the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics with four-component fermions. The three-loop correction is finite and gauge invariant but the four-loop one has singularities except in the Feynman gauge where it is also finite. Our results explicitly show that, up to four loops, gauge-dependent terms are completely determined by lower order ones in agreement with the Landau-Khalatnikov-Fradkin transformation., Comment: 11+4 pages

We study the gauge-covariance of the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics in the framework of dimensional regularization in d=3-2\ep. Assuming the finiteness of the quenched perturbative expansion, that is the existence of the limit \ep \to 0, we state that, exactly in d=3, all odd perturbative coefficients, starting with the third order one, should be zero in any gauge., Comment: 17 pages, no figures

We report some results of calculations of massless and massive Feynman integrals particularly focusing on difference equations for coefficients of for their series expansions, Comment: 51 pages; contribution to the proceedings of Helmholtz International Summer School "Quantum Field Theory at the Limits: from Strong Fields to Heavy Quarks" (July 22 - August 2, 2019; Dubna, Russia)

We study the new relation [1] between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations for the first Mellin moments D_{q,g}(\mu^2) of the fragmentation functions, which correspond to the average multiplicities of hadrons in jets initiated by quarks and gluons, respectively. This relation is shown to lead to probabilistic properties of the properly rescaled parton jet multiplicities obtained from standard ones by extracting the quark and gluon "color charges" C_F and C_A, respectively., Comment: 17 pages

We show an exact formula obtained in [1], which relates hatted and standard zeta-values to all orders of perturbation theory. The formula is based on the Landau-Khalatnikov-Fradkin (LKF) transformation between the massless propagators of charged particles interacting with gauge fields, in two different gauges., Comment: 8 pages; contribution to the proceedings of International Bogolyubov Conference "Problems of Theoretical and Mathematical Physics" (September 9 - 13, 2019; Dubna, Russia); based on arXiv:1906.10930

We study the gauge-covariance of the massless fermion propagator in reduced Quantum Electrodynamics (QED). Starting from its value in some gauge, we evaluate an all order expression for it in another gauge by means of the Landau-Khalatnikov-Fradkin transformation. We find that the weak coupling expansions thus derived are in perfect agreement with the exact calculations. We also prove that the fermion anomalous dimension of reduced QED is gauge invariant to all orders of perturbation theory except for the first one., Comment: (v2) 11 pages, two-column format, no figure, published in Phys. Rev. D, edits in text (some per referee's comments) and references added, no change in results. (v1) 23 pages, no figure

We present a nonlinear modification of the evolution of the gluon density, obtained at small x from the Berger-Block-Tan form of the deep inelastic structure function F2 in the leading order of perturbation theory., Comment: 7 pages

We use the Bessel-inspired behavior of parton densities at small Bjorken $x$ values, obtained in the case of the flat initial conditions for DGLAP evolution equations in the double scaling QCD approximation (DAS), to evaluate the transverse momentum dependent (TMD, or unintegrated) quark and gluon distribution functions in a proton. The calculations are performed analytically using the Kimber-Martin-Ryskin (KMR) prescription with different implementation of kinematical constraint, reflecting the angular and strong ordering conditions. The relations between the differential and integral formulation of the KMR approach is discussed. Several phenomenological applications of the proposed TMD parton densities to the LHC processes are given., Comment: 24 pages, 9 figures

DGLAP and BFKL equations are among the cornestones of the contemporary QCD. Moreover, they also played an important role in the recent studies of integrability structure of $\mathcal{N}=4$ SYM. Here, we review the results obtained along this way together with a brief account of approaches and methods used., Comment: 35 pages, will be published in a book dedicated to the memory of Lev Lipatov

In this paper we consider two-loop two-, three- and four-point diagrams with elliptic structure in the case of two different masses $m$ and $M$. The latter diagrams generally arise within NRQCD matching procedures and are relevant for parapositronium decay and top pair production at threshold. We present the obtained results in several different representations: series solution with binomial coefficients, integral representation and representation in terms of generalized hypergeometric functions. The results are valid up to $\mathcal{O}(\varepsilon)$ terms in $d=4-2\varepsilon$ space-time dimensions. In the limit of equal masses $m=M$ the obtained results are written in terms of elliptic constants with explicit series representation., Comment: 31 pages, 2 figures, matches journal version

The Landau-Khalatnikov-Fradkin (LKF) transformation is a powerful and elegant transformation allowing to study the gauge dependence of the propagator of charged particles interacting with gauge fields. With the help of this transformation, we derive a non-perturbative identity between massless propagators in two different gauges. From this identity, we find that the corresponding perturbative series can be exactly expressed in terms of a hatted transcendental basis that eliminates all even Euler $\zeta$-functions. This explains the mystery of even $\zeta$-values observed in multi-loop calculations of Euclidean massless correlators for almost three decades now. Our construction further allows us to derive an exact formula relating hatted and standard $\zeta$-functions to all orders of perturbation theory., Comment: (v2) 9 pages, no figure, published in PRD, few edits in text (some per referee's comments) and references added, no change in results. (v1) 9 pages, no figure

We present a method to extract, in the leading and next-to-leading order approximations, the longitudinal deep-inelastic scattering structure function FL(x,Q2) from the experimental data by relying on a Froissart-bounded parametrization of the transversal structure function F2(x,Q2) and, partially, on the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations. Particular attention is paid on kinematics of low and ultra low values of the Bjorken variable x. Analytical expressions for FL(x,Q2) in terms of the effective parameters of the parametrization of F2(x,Q2) are presented explicitly. We argue that the obtained structure functions FL(x,Q2) within both, the leading and next-to-leading order approximations, manifestly obey the Froissart boundary conditions. Numerical calculations and comparison with available data from ZEUS and H1-Collaborations at HERA demonstrate that the suggested method provides reliable structure functions FL(x,Q2) at low x in a wide range of the momentum transfer (1 GeV2 < Q2 < 3000 GeV2) and can be applied as well in analyses of ultra-high energy processes with cosmic neutrinos., Comment: 30 pages, 4 figures

Dynamical chiral symmetry breaking (D$\chi$SB) is studied within ($2+1$)-dimensional QED with $N$ four-component fermions. The leading and next-to-leading orders of the $N$ expansion were computed exactly in Refs.~[\onlinecite{Gusynin:2016som,Kotikov:2016prf}] in an arbitrary non-local gauge. In this addendum to [\onlinecite{Kotikov:2016prf}], we show that the resummation of the wave-function renormalization constant at the level of the gap equation yields a {\it complete} cancellation of the gauge dependence of the critical fermion flavour number resulting in: $N_c= 2.8469$, which is such that D$\chi$SB takes place for $N

Experimental data obtained for the polarized Bjorken sum rule (BSR) $\Gamma_1^{p-n}(Q^2)$ are fitted by using predictions derived within a truncated operator product expansion (OPE) approach to QCD. Four QCD versions are considered: perturbative QCD (pQCD) in the MSbar scheme, Analytic Perturbation Theory (APT), and 2$\delta$ and 3$\delta$ analytic QCD versions. In contrast to pQCD, these QCD variants do not have Landau singularities at low positive $Q^2$, which facilitates the fitting procedure significantly. The fitting procedure is applied first to the experimental data of the inelastic part of BSR, and the known elastic contributions are added after the fitting. In general, when 2$\delta$ and 3$\delta$ QCD coupling is used the fitted curves give the best results, within the $Q^2$-range of the fit as well as in extended $Q^2$-intervals. When the fitting procedure is applied to the total BSR, i.e., to the sum of the experimental data and the elastic contribution, the quality of the results deteriorates significantly., Comment: 29 pages, 8 figures; to appear in EPJ C

The longitudinal structure function FL(x,Q2) is extracted at low values of the Bjorken variable x from the Berger-Block-Tan parametrization of F2(x,Q2). The obtained FL(x,Q2) does not violate the high-energy asymptotic Froissart boundary and is in a reasonable good agreement with the available experimental data., Comment: 6 pages, 1 figure

The antishadowing behavior of the sea and valence quark densities in nuclei is investigated in the framework of the rescaling model at the values x ~ 0.1 of the Bjorken variable x., Comment: 5 pages, 1 figure