Two-Loop Massive Operator Matrix Elements for Polarized and Unpolarized Deep-Inelastic Scattering

Abstract

The heavy-flavor corrections to deeply inelastic structure functions are very important for the range of small values of x and do contribute there on the level of 20–40%. They have to be known at the same level of accuracy as the light-flavor contributions for precision measurements of ΛQCD [2] and the parton distributions. The next-to-leading order corrections were given semi-analytically in [3] for the general kinematic range. Fast and accurate implementations of these corrections in Mellin-space were given in [4]. In the region Q >> m, the heavy flavor Wilson coefficients were derived analytically to O(αs) [5, 6]. Here Q 2 denotes the virtuality of the gauge boson exchanged in deeply–inelastic scattering and m is the mass of the heavy quark. In this note we summarize the results of a first re-calculation of the operator matrix elements (OMEs) in [7,8]. The calculation is being performed in Mellinspace using harmonic sums [9, 10] without applying the integration-by-parts technique. In this way, we can significantly compactify both, the intermediary and final results. We agree with the results in [5, 6]. The unpolarized and polarized O(αs) massive OMEs can be used to calculate the asymptotic heavy-flavor Wilson coefficients for F2(x,Q ) and g1(x,Q ) to O(αs) [5–8], and for FL(x,Q ) to O(αs) [11].