$O(α_s^2)$ Timelike Wilson Coefficients for Parton-Fragmentation Functions in Mellin Space

Details $O(α_s^2)$ Timelike Wilson Coefficients for Parton-Fragmentation Functions in Mellin Space $O(α_s^2)$ Timelike Wilson Coefficients for Parton-Fragmentation Functions in Mellin Space

2006-04-03

arxiv.org/abs/hep-ph/0604019v1

Nucl.Phys.B749:1-24,2006

Physics

High Energy Physics

High Energy Physics - Phenomenology

25 pages

Scientific paper

10.1016/j.nuclphysb.2006.04.032

We calculate the Mellin moments of the $O(\alpha_s^2)$ coefficient functions for the unpolarized and polarized fragmentation functions. They can be expressed in terms of multiple finite harmonic sums of maximal weight {\sf w = 4}. Using algebraic and structural relations between harmonic sums one finds that besides the single harmonic sums only three basic sums and their derivatives w.r.t. the summation index contribute. The Mellin moments are analytically continued to complex values of the Mellin variable. This representation significantly reduces the large complexity being present in $x$--space calculations and allow very compact and fast numerical implementations.

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