376 research outputs found
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
A calculation of the three-loop helicity-dependent splitting functions in QCD
We have calculated the complete matrix of three-loop helicity-difference
(`polarized') splitting functions Delta P_ik^(2), i,k = q,g, in massless
perturbative QCD. In this note we briefly discuss some properties of the
polarized splitting functions and our non-standard determination of the
hitherto missing lower-row quantities Delta P_gq^(2) and Delta P_gg^(2). The
resulting next-to-next-to-leading order (NNLO) corrections to the evolution of
polarized parton distributions are illustrated and found to be small even at
rather large values of the strong coupling constant alpha_s.Comment: 10 pages, LaTeX (PoS style), 4 eps-figures. Proceedings of `Loops &
Legs 2014', Weimar (Germany), April/May 201
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