Two-Dimensional Transverse-Momentum Subtraction and Semi-Inclusive Deep-Inelastic Scattering at N$^3$LO in QCD

TL;DR

This paper presents the first N$^3$LO calculation of unpolarized semi-inclusive deep-inelastic scattering (SIDIS) in QCD, using a novel two-dimensional transverse-momentum subtraction method, enabling high-precision nucleon structure studies.

Contribution

It introduces a new subtraction technique for N$^3$LO SIDIS calculations, improving theoretical accuracy and facilitating future polarized SIDIS analyses.

Findings

N$^3$LO corrections are generally moderate but significant near thresholds.

The method shows excellent perturbative convergence and reduced scale dependence.

Framework supports arbitrary cuts, aiding precision nucleon tomography at EIC.

Abstract

Identified hadron production is essential for the study of nucleon structure and QCD hadronization at high energies. We present the first calculation of unpolarized semi-inclusive deep-inelastic scattering (SIDIS) at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. Our calculation is based on a novel method of two-dimensional transverse-momentum subtraction motivated by QCD factorization of soft and collinear singularities. The N$^3$LO corrections are moderate in general but can be significant in threshold regions, and exhibit excellent perturbative convergence and reduced scale variations. The fully differential framework allows for arbitrary selection cuts and directly enables precision nucleon tomography at the upcoming Electron-Ion Collider, establishing the theory foundation needed to match the anticipated experimental accuracy. Generalization of the method to calculations of polarized SIDIS is also feasible.