The massless three-loop Wilson coefficients for the deep-inelastic structure functions F2, FL, xF3 and g1
J. Blümlein, Peter Marquard, Carsten Schneider, Kay Schönwald
Abstract
A bstract We calculate the massless unpolarized Wilson coefficients for deeply inelastic scattering for the structure functions F 2 ( x, Q 2 ) , F L ( x, Q 2 ) , xF 3 ( x, Q 2 ) in the $$ \overline{\textrm{MS}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> scheme and the polarized Wilson coefficients of the structure function g 1 ( x, Q 2 ) in the Larin scheme up to three-loop order in QCD in a fully automated way based on the method of arbitrary high Mellin moments. We work in the Larin scheme in the case of contributing axial-vector couplings or polarized nucleons. For the unpolarized structure functions we compare to results given in the literature. The polarized three-loop Wilson coefficients are calculated for the first time. As a by-product we also obtain the quarkonic three-loop anomalous dimensions from the O (1 /ε ) terms of the unrenormalized forward Compton amplitude. Expansions for small and large values of the Bjorken variable x are provided.