Some methods to evaluate complicated Feynman integrals

I discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method.Comment: 2 pages, 1 figure, latex. Talk presented at the 8th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2002), Moscow, Russia, June 200

Analytic two-loop results for selfenergy- and vertex-type diagrams with one non-zero mass

For a large class of two-loop selfenergy- and vertex-type diagrams with only one non-zero mass ($M$) and the vertices also with only one non-zero external momentum squared ($q^2$) the first few expansion coefficients are calculated by the large mass expansion. This allows to `guess' the general structure of these coefficients and to verify them in terms of certain classes of `basis elements', which are essentially harmonic sums. Since for this case with only one non-zero mass the large mass expansion and the Taylor series in terms of $q^2$ are identical, this approach yields analytic expressions of the Taylor coefficients, from which the diagram can be easily evaluated numerically in a large domain of the complex $q^2-$plane by well known methods. It is also possible to sum the Taylor series and present the results in terms of polylogarithms.Comment: LaTeX, 27 pages + 3 ps figures, uses axodraw.sty, some references reviste

Small x behaviour of parton distributions with soft initial conditions

We present an analytical parametrization of the QCD description of the small x behaviour of parton distribution functions in the leading twist approximation of the Wilson operator product expansion, in the case of soft initial conditions. The results are in very good agreement with deep inelastic scattering experimental data from HERA.Comment: 21 pages, latex + 3 ps figure

Twist 3 of the sl(2) sector of N=4 SYM and reciprocity respecting evolution

We consider the bosonic sl(2) sector of the maximally supersymmetric N=4 SYM model and show that anomalous dimension of the twist-3 single-trace composite operators built of scalar fields, recently calculated up to the four-loop order, can be generated by a compact reciprocity respecting evolution kernel.Comment: 18 pages, 1 eps figur

Two-loop sunset diagrams with three massive lines

In this paper, we consider the two-loop sunset diagram with two different masses, m and M, at spacelike virtuality q^2 = -m^2. We find explicit representations for the master integrals and an analytic result through O(epsilon) in d=4-2epsilon space-time dimensions for the case of equal masses, m = M.Comment: 11 page

About calculation of massless and massive Feynman integrals

We report some results of calculations of massless and massive Feynman integrals particularly focusing on difference equations for coefficients of for their series expansionsComment: 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