FORM facts

Some of the new features of the symbolic manipulation system FORM are discussed. Then some recent results running its multithreaded version TFORM are shown. Finally the plans for the future are presented.Comment: 6 pages. Talk presented at the Loops and Legs 2010 worksho

Harmonic sums, Mellin transforms and Integrals

This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that are encountered in Feynman diagram calculations. Together with results for the values of the higher harmonic series at infinity the presented algorithms can be used for the symbolic evaluation of whole classes of integrals that were thus far intractable. Also many of the sums that had to be evaluated seem to involve new results. Most of the algorithms have been programmed in the language of FORM. The resulting set of procedures is called SUMMER.Comment: 31 pages LaTeX, for programs, see http://norma.nikhef.nl/~t68/summe

Deep Inelastic Structure Functions at two Loops

We present the analytic calculation of the Mellin moments of the structure functions F_2, F_3 and F_L in perturbative QCD up to second order corrections and in leading twist approximation. We calculate the 2-loop contributions to the anomalous dimensions of the singlet and non-singlet operator matrix elements and the 2-loop coefficient functions of F_2, F_3 and F_L. We perform the inverse Mellin transformation analytically and find our results in agreement with earlier calculations in the literature by Zijlstra and van Neerven.Comment: 45 pages LaTe

Deep-inelastic structure functions: Reconstruction from Mellin moments

We summarize the method of calculating Mellin moments of deep-inelastic structure functions in perturbative QCD. We briefly discuss all steps to a complete analytical reconstruction of the perturbative corrrections in x-space.Comment: 6 pages LaTeX, presented at LL2000, Bastei (Germany

Pomerons and Jet Events at HERA

We study two and three jet events with a large rapidity gap at HERA. Unlike in the Ingelman-Schlein approach we do not adscribe a structure to the Pomeron. Instead, the coupling of the Pomeron to quarks or gluons is taken pointlike, which makes the model easy to test: the only degrees of freedom are the coupling constants of the Pomeron to the quarks or the gluons and a cutoff procedure to keep the Pomeron-gluon coupling well behaved.Comment: Latex fil

The Quark Form Factor at Higher Orders

We study the electromagnetic on-shell form factor of quarks in massless perturbative QCD. We derive the complete pole part in dimensional regularization at three loops, and extend the resummation of the form factor to the next-to-next-to-leading contributions. These results are employed to evaluate the infrared finite absolute ratio of the time-like and space-like form factors up to the fourth order in the strong coupling constant. Besides for the pole structure of higher-loop QCD amplitudes, our new contributions to the form factor are also relevant for the high-energy limit of massive gauge theories like QED. The highest-transcendentality component of our results confirms a result recently obtained in N=4 Super-Yang-Mills theory.Comment: 16 pages, 1 figure, Late