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

TL;DR

This paper extends the threshold resummation formalism for semi-inclusive deep-inelastic scattering to N$^{3}$LL accuracy, providing approximate N$^{3}$LO corrections that demonstrate perturbative stability and modest impact on the cross section.

Contribution

It introduces the N$^{3}$LL resummation formalism for SIDIS and derives approximate N$^{3}$LO corrections including three-loop hard factors, enhancing precision in theoretical predictions.

Findings

Approximate N$^{3}$LO corrections cause modest changes in the SIDIS cross section.

The perturbative series shows good stability with the new corrections.

The formalism includes all threshold-enhanced and constant terms in Mellin space.

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.