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

The property of maximal transcendentality in the N=4 SYM

We show results for the universal anomalous dimension gamma_{uni}(j) of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory in the first three orders of perturbation theory. These expressions are obtained by extracting the most complicated contributions from the corresponding anomalous dimensions in QCD.Comment: 6 pages, published in the Proceedings of International Bogolyubov Conference "Problems of Theoretical and Mathematical Physics" (dedicated to the 100th anniversary of the birth of N.N. Bogolyubov (1909-1992)), Dubna, Russia, August 21 - 27, 2009 (Phys.Part.Nucl. in press

Compact analytical form for a class of three-loop vacuum Feynman diagrams

We present compact, fully analytical expressions for singular parts of a class of three-loop diagrams which cannot be factorized into lower-loop integrals. As a result of the calculations we obtain the analytical expression for the three-loop effective potential of the massive O(N) \phi^4 model presented recently by J.-M.Chung and B.K.Chung, Phys.Rev. D56, 6508 (1997).Comment: 5 pages, latex + 1 ps figur

Asymptotic neutrino-nucleon cross section and saturation effects

In this paper we present a simple analytic expression for the (spin-averaged) neutrino-nucleon cross section for ultra-high energies at twist-2, obtained as the asymptotic limit of our previous findings. This expression gives values for the cross section in remarkable numerical agreement with the previous numerical evaluation in the energy region relevant for forthcoming neutrino experiments. Moreover, we discuss the role and the relevance of saturation and recombination effects in our approach, in comparison with other recent suggestions.Comment: 19 pages, 2 figure