Threshold resummation at N${}^3$LL accuracy and approximate N${}^3$LO corrections to semi-inclusive DIS

Abstract

We advance the threshold resummation formalism for semi-inclusive deep-inelastic scattering (SIDIS) to next-to-next-to-next-to-leading logarithmic (N${}^3$LL) order, including the three-loop hard factor. We expand the results in the strong coupling to obtain approximate next-to-next-to-next-to-leading order (N${}^3$LO) corrections for the SIDIS cross section. In Mellin moment space, these corrections include all terms that are logarithmically enhanced at threshold, or that are constant. We also consider a set of corrections that are suppressed near threshold. Our numerical estimates show modest changes of the cross section by the approximate N${}^3$LO terms, suggesting a very good perturbative stability of the SIDIS process.

Comments: 25 pages, 2 figures