Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators

We present an algorithm for the analytical evaluation of dimensionally regularized massless on-shell double box Feynman diagrams with arbitrary polynomials in numerators and general integer powers of propagators. Recurrence relations following from integration by parts are solved explicitly and any given double box diagram is expressed as a linear combination of two master double boxes and a family of simpler diagrams. The first master double box corresponds to all powers of the propagators equal to one and no numerators, and the second master double box differs from the first one by the second power of the middle propagator. By use of differential relations, the second master double box is expressed through the first one up to a similar linear combination of simpler double boxes so that the analytical evaluation of the first master double box provides explicit analytical results, in terms of polylogarithms \Li{a}{-t/s}, up to $a=4$, and generalized polylogarithms $S_{a,b}(-t/s)$, with $a=1,2$ and $b=2$, dependent on the Mandelstam variables $s$ and $t$, for an arbitrary diagram under consideration.Comment: LaTeX, 16 pages; misprints in ff. (8), (24), (30) corrected; some explanations adde

Two-loop QCD corrections of the massive fermion propagator

The off-shell two-loop correction to the massive quark propagator in an arbitrary covariant gauge is calculated and results for the bare and renormalized propagator are presented. The calculations were performed by means of a set of new generalized recurrence relations proposed recently by one of the authors. From the position of the pole of the renormalized propagator we obtain the relationship between the pole mass and the \bar{MS} mass. This relation confirms the known result by Gray et al.. The bare amplitudes are given for an arbitrary gauge group and for arbitrary space-time dimensions.Comment: 18 pages LaTeX, misprints in formula (12) are correcte

Irrational constants in positronium decays

We establish irrational constants, that contribute to the positronium lifetime at $O(\alpha)$ and $O(\alpha^2)$ order. In particular we show, that a new type of constants appear, which are not related to Euler--Zagier sums or multiple $\zeta$ values.Comment: Presented at 9th Workshop on Elementary Particle Theory: Loops and Legs in Quantum Field Theory, Sondershausen, 20-25 Apr 2008. 6 pages, 3 figure

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

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

Techniques for calculating two loop diagrams

Fleischer J, Veretin OL. Techniques for calculating two loop diagrams. 1998