Polarized semi-inclusive deep-inelastic scattering at NNLO in QCD

TL;DR

This work delivers the first full NNLO QCD corrections to the coefficient functions for longitudinally polarized SIDIS, enabling consistent NNLO analyses of polarized parton distributions and fragmentation functions. It outlines a rigorous analytical calculation using the HVBM/Larin scheme, with RR, RV, and VV contributions reduced to master integrals and expressed via harmonic polylogarithms, followed by a scheme transformation to $ar{ ext{MS}}$. The authors validate the results through multiple consistency checks, reproduce the inclusive $g_1$ result, and demonstrate the numerical impact on spin asymmetries such as $A_1^{pi^+}$—notably at low $x$ and low $Q^2$—and predict strong perturbative convergence at EIC-like kinematics. This work thereby enables precision, NNLO-level determinations of polarized PDFs and FFs from SIDIS data, sharpening the extraction of the proton's spin structure.

Abstract

Semi-inclusive hadron production in longitudinally polarized deep-inelastic lepton-nucleon scattering is a powerful tool for resolving the quark flavor decomposition of the proton's spin structure. We present the full next-to-next-to-leading order (NNLO) QCD corrections to the coefficient functions of polarized semi-inclusive deep-inelastic scattering (SIDIS) in analytical form, enabling the use of SIDIS measurements in precision studies of the proton spin structure. The numerical impact of these corrections is illustrated by a comparison with data of polarized single-inclusive hadron spectra from the DESY HERMES and CERN COMPASS experiments.

Figures (3)

• Figure 1: Asymmetries $A_1^{\pi^+}$ at different perturbative orders compared to data from COMPASS COMPASS:2010hwr and HERMES HERMES:2018awh, computed using NLO PDFs and FFs (left) and NNLO PDFs and FFs (right).
• Figure 2: Channel decomposition of theory predictions for $g_1^{\pi^+}$ with COMPASS kinematics.
• Figure 3: Longitudinally polarized SIDIS structure function $g_1^{\pi^+}$ for EIC kinematics at $\sqrt{s}=45$ GeV, evaluated at different perturbative orders.