Soft and virtual corrections to semi-inclusive DIS up to four loops in QCD

TL;DR

This paper derives four-loop soft and virtual QCD corrections for semi-inclusive deep-inelastic scattering (SIDIS), demonstrating high perturbative stability and minimal impact on the cross section, thus enhancing theoretical precision.

Contribution

It provides the first complete four-loop soft and collinear corrections to SIDIS cross sections, incorporating next-to-leading power effects and confirming perturbative stability.

Findings

Four-loop corrections have a small impact on the SIDIS cross section.

The results show reduced dependence on renormalization and factorization scales.

Perturbative predictions remain stable at four-loop order.

Abstract

We apply the threshold resummation formalism for semi-inclusive deep-inelastic scattering (SIDIS) to derive the soft and virtual corrections for the SIDIS cross section up to four loops in QCD. Using the recently computed next-to-next-to-leading order QCD corrections for the SIDIS cross section together with known results for the form factor and splitting functions in QCD up to four loops, we derive the complete soft and collinear contributions to the SIDIS coefficient functions at four-loop order. We also include systematically the next-to-leading power corrections, which are suppressed near threshold. The numerical analysis of the new four-loop corrections shows a small effect on the cross section underpinning the very good perturbative stability of the SIDIS process at that order in perturbation theory, including the reduced dependence on the renormalization and factorization scales $\mu_R$ and $\mu_F$.