Series and epsilon-expansion of the hypergeometric functions

Recent progress in analytical calculation of the multiple [inverse, binomial, harmonic] sums, related with epsilon-expansion of the hypergeometric function of one variable are discussed.Comment: 5 pages, to appear in the proceedings of 7th DESY Workshop on Elementary Particle Theory "Loops and Legs in Quantum Field Theory", April 25 -30, 2004, Zinnowitz (Usedom Island), German

Geometrical methods in loop calculations and the three-point function

A geometrical way to calculate N-point Feynman diagrams is reviewed. As an example, the dimensionally-regulated three-point function is considered, including all orders of its epsilon-expansion. Analytical continuation to other regions of the kinematical variables is discussed.Comment: 6 pages, LaTeX, 3 eps figures, contribution to proceedings of ACAT2005 (Zeuthen, May 2005

Analytical evaluation of certain on-shell two-loop three-point diagrams

An analytical approach is applied to the calculation of some dimensionally-regulated two-loop vertex diagrams with essential on-shell singularities. Such diagrams are important for the evaluation of QED corrections to the muon decay, QCD corrections to top quark decays t->W^{+}b, t->H^{+}b, etc.Comment: 2 pages, LaTeX, contribution to proceedings of ACAT2002 (Moscow, June 2002

Hypergeometric representation of the two-loop equal mass sunrise diagram

A recurrence relation between equal mass two-loop sunrise diagrams differing in dimensionality by 2 is derived and it's solution in terms of Gauss' 2F1 and Appell's F_2 hypergeometric functions is presented. For arbitrary space-time dimension d the imaginary part of the diagram on the cut is found to be the 2F1 hypergeometric function with argument proportional to the maximum of the Kibble cubic form. The analytic expression for the threshold value of the diagram in terms of the hypergeometric function 3F2 of argument -1/3 is given.Comment: 10 page

Four-point function in general kinematics through geometrical splitting and reduction

It is shown how the geometrical splitting of N-point Feynman diagrams can be used to simplify the parametric integrals and reduce the number of variables in the occurring functions. As an example, a calculation of the dimensionally-regulated one-loop four-point function in general kinematics is presented.Comment: 8 pages, 9 figures, contribution for proceedings of ACAT 2017 (Seattle, USA, August 21-25, 2017). arXiv admin note: substantial text overlap with arXiv:1605.0482

On evaluation of two-loop self-energy diagram with three propogator

Small momentum expansion of the "sunset" diagram with three different masses is obtained. Coefficients at powers of $p^2$ are evaluated explicitly in terms of dilogarithms and elementary functions. Also some power expansions of "sunset" diagram in terms of different sets of variables are given.Comment: 9 pages, LaTEX, MSU-PHYS-HEP-Lu3/9

One-loop results for the quark-gluon vertex in arbitrary dimension

Results on the one-loop quark-gluon vertex with massive quarks are reviewed, in an arbitrary covariant gauge and in arbitrary space-time dimension. We show how it is possible to get on-shell results from the general off-shell expressions. The corresponding Ward-Slavnov-Taylor identity is discussed.Comment: 6 pages, LaTeX, including 1 figure, uses epsfig, requires espcrc2.sty, contribution to the Zeuthen Workshop "Loops and Legs in Gauge Theories" (Bastei, Germany, April 2000

Causal construction of the massless vertex diagram

The massless one-loop vertex diagram is constructed by exploiting the causal structure of the diagram in configuration space, which can be translated directly into dispersive relations in momentum space.Comment: 14 pages, LATEX with style file, corresponds to published versio