Approximate NNLO QCD corrections to semi-inclusive DIS

TL;DR

This paper develops approximate NNLO QCD corrections for semi-inclusive DIS using threshold resummation, improving theoretical precision and reducing scale dependence in predictions.

Contribution

It introduces a full NNLL resummation formalism for semi-inclusive DIS and derives approximate NNLO corrections by expanding this resummation.

Findings

Approximate NNLO corrections significantly impact predictions.

Reduction in theoretical scale dependence.

Enhanced understanding of threshold effects in SIDIS.

Abstract

We determine approximate next-to-next-to-leading order (NNLO) corrections to unpolarized and polarized semi-inclusive DIS. They are derived using the threshold resummation formalism, which we fully develop to next-to-next-to-leading logarithmic (NNLL) accuracy, including the two-loop hard factor. The approximate NNLO terms are obtained by expansion of the resummed expression. They include all terms in Mellin space that are logarithmically enhanced at threshold, or that are constant. In terms of the customary SIDIS variables $x$ and $z$ they include all double distributions (that is, "plus" distributions and $\delta$-functions) in the partonic variables. We also investigate corrections that are suppressed at threshold and we determine the dominant terms among these. Our numerical estimates suggest much significance of the approximate NNLO terms, along with a reduction in scale dependence.