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The results of calculation of the three-loop radiative correction to the renormalization constant of fermion masses for non-abelian gauge theory interacting with fermions are presented. Dimensional regularization and the 't Hooft minimal subtraction scheme are used. The method of calculation is described in detail. The renormalization group function $\gamma_m$ determining the behavior of the effective mass of fermions is presented. The anomalous dimensions of fermions for QED and QCD up to three loops are given. All calculations were performed on a computer with the help of the SCHOOONSCHIP system for analytical manipulations. The present text was published in 1982 as a JINR Communication, JINR-P2-82-900 (in russian)., Comment: 11 pages

We report on the measurement of the beam asymmetry $\Sigma$ for the reactions $\vec{\gamma}p\rightarrow p\eta$ and $\vec{\gamma}p \rightarrow p\eta^{\prime}$ from the GlueX experiment, using an 8.2--8.8 GeV linearly polarized tagged photon beam incident on a liquid hydrogen target in Hall D at Jefferson Lab. These measurements are made as a function of momentum transfer $-t$, with significantly higher statistical precision than our earlier $\eta$ measurements, and are the first measurements of $\eta^{\prime}$ in this energy range. We compare the results to theoretical predictions based on $t$--channel quasi-particle exchange. We also compare the ratio of $\Sigma_{\eta}$ to $\Sigma_{\eta^{\prime}}$ to these models, as this ratio is predicted to be sensitive to the amount of $s\bar{s}$ exchange in the production. We find that photoproduction of both $\eta$ and $\eta^{\prime}$ is dominated by natural parity exchange with little dependence on $-t$., Comment: 18 pages, 7 figures

Based on the analysis of approaches to the definition of professional competencies of IT students the competence in programming of bachelor of informatics is proposed. Due to the standard of training in 040302 "Informatics" and Computing Curricula 2001 it was defined the content and structure of the competence in programming of bachelor of informatics. The system of content modules providing its formation was designed. The contribution of regulatory competencies of bachelor of informatics in the formation of competence in programming is defined. The directions of formation of competence in programming in the cloudy-oriented learning environment are proposed., Comment: 18 pages, 4 figures, in Ukrainian

We develop a theoretical method for solving Maxwell's equations to obtain the frequency spectra of inhomogeneous and asymmetric cavity resonators using a couple of effective Debye-type potentials. The structure we study specifically is the layered spherical cavity resonator with symmetrically or asymmetrically inserted inner dielectric sphere. The comparison of the exact numerical results obtained for the frequency spectrum of layered cavity resonator with centrosymmetrically inserted sphere and the spectrum found from the suggested theory reveals good agreement at the initial part of the frequency axis. The coincidence accuracy depends on the number of trial resonant modes that we use while approving our method numerically., Comment: 7 pages, 2 figures

Scattering of TM-polarized surface plasmon-polariton waves (PPW) by a finite segment of the metal-vacuum interface with randomly fluctuating surface impedance is examined. Solution of the integral equation relating the scattered field with the field of the incident PPW, valid for arbitrary scattering intensity and arbitrary dissipative characteristics of the conductive medium, is analyzed. As a measure of the PPW scattering, the Hilbert norm of the integral scattering operator is used. The strength of the scattering is shown to be determined not only by the parameters of the fluctuating impedance (dispersion, correlation radius and the length of the inhomogeneity region) but also by the conductivity of the metal. If the scattering operator norm is small, the PPW is mainly scattered into the vacuum, thus losing its energy through the excitation of quasi-isotropic bulk Norton-type waves above the conducting surface. The intensity of the scattered field is expressed in terms of the random impedance pair correlation function, whose dependence on the incident and scattered wavenumbers shows that in the case of random-impedance-induced scattering of PPW it is possible to observe the effect analogous to Wood's anomalies of wave scattering on periodic gratings. Under strong scattering, when the scattering operator norm becomes large compared to unity, the radiation into free space is strongly suppressed, and, in the limit, the incoming PPW is almost perfectly back-reflected from the inhomogeneous part of the interface. This suggests that within the model of a dissipation-free conducting medium, the surface polariton is unstable against arbitrary small fluctuations of the medium polarizability. Transition from quasi-isotropic weak scattering to nealy back-reflection under strong fluctuations of the impedance is interpreted in terms of Anderson localization., Comment: 8 pages, 2 figures

The massless one-loop box integral with arbitrary indices in arbitrary space-time dimension $d$ is shown to reduce to a sum over three generalised hypergeometric functions. This result follows from the solution to the third order differential equation of hypergeometric type. To derive the differential equation, the Gr\"obner basis technique for integrals with noninteger powers of propagators was used. A complete set of recurrence relations from the Gr\"obner basis is presented. The first several terms in the $\varepsilon =(4-d)/2$ expansion of the result are given., Comment: 9 pages, 1figure

We present short review of two methods for obtaining functional equations for Feynman integrals. Application of these methods for finding functional equations for one- and two- loop integrals is described in detail. It is shown that with the aid of functional equations Feynman integrals in general kinematics can be expressed in terms of simpler integrals. Similarities between functional equations for Feynman integrals and addition theorem for Abel integrals are shortly discussed., Comment: 11 pages, 2 figures, PdfLatex

We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example., Comment: 8 pages, 1 figure

New methods for obtaining functional equations for Feynman integrals are presented. Application of these methods for finding functional equations for various one- and two- loop integrals described in detail. It is shown that with the aid of functional equations Feynman integrals in general kinematics can be expressed in terms of simpler integrals., Comment: 20 pages, 4 jpeg figures

Using the DIANA data on the charge-exchange reaction $K^+n \rightarrow pK^0$ on a bound neutron, in which the s-channel formation of the pentaquark baryon $\Theta^+(1538)$ has been observed, we analyze the dependence of the background-subtracted $\Theta^+ \rightarrow pK^0$ signal on the $K^0$ emission angle in the $pK^0$ rest frame. In order to describe the observed $\cos\Theta_K^\mathrm{cms}$ distribution, invoking the interference between the nonresonant s-wave and the $\Theta^+$-mediated higher-wave contributions to the amplitude of the charge-exchange reaction is required at a 2.8$\sigma$ level. The spin--parity assignment of 1/2$^-$ for the $\Theta^+$ baryon is ruled out at a statistical level of 2.9 standard deviations. A physically-meaningful selection in $\cos\Theta_K^\mathrm{cms}$ based on the observed angular dependence of the $\Theta^+ \rightarrow pK^0$ signal allows to boost the statistical significance of the signal up to 7.1 standard deviations. This is far in excess of previously reported signals and renders the $\Theta^+$ existence more credible., Comment: 13 pages, 7 figures