Single-valued representation of unpolarized and polarized semi-inclusive deep inelastic scattering at next-to-next-to-leading order

TL;DR

This paper simplifies the complex NNLO QCD calculations for SIDIS by expressing them with single-valued polylogarithms, creating a unified, more concise formula applicable across all kinematic regions.

Contribution

It introduces a unified analytic expression for SIDIS NNLO coefficients using single-valued polylogarithms, removing previous case distinctions.

Findings

Unified NNLO SIDIS coefficients across all kinematic regions

Reduction of expression length by 30% to 60%

Simplified analytic form for practical computations

Abstract

We revisit the recently published analytic results for unpolarized and polarized semi-inclusive deep inelastic scattering (SIDIS) at next-to-next-to-leading order (NNLO) in QCD. These expressions for the hard scattering coefficients contain case distinctions in the kinematic $(x,z)$ plane splitting the analytic result in four regions. By re-expressing the coefficient functions in terms of single-valued polylogarithms we remove these case distinctions and can present a unified result valid in the entire kinematic range of SIDIS. This reduces the length of the overall expressions by 30% to 60%.