Polarized Semi-Inclusive Deep-Inelastic Scattering at $\mathcal O(\alpha_s^3)$ in QCD

Abstract

Unraveling the partonic origin of the proton spin requires precise determinations of polarized parton distribution functions (PDFs), which depend on comparably precise theoretical predictions for polarized scattering, particularly in view of the high-precision measurements anticipated at the future Electron-Ion Collider. We present the first next-to-next-to-next-to-leading order (N$^3$LO) QCD predictions for longitudinally polarized semi-inclusive deep-inelastic scattering (SIDIS) in a fully differential form, together with next-to-next-to-leading order predictions for the hadron transverse-momentum spectrum. These results are obtained by extending the two-dimensional transverse-momentum subtraction framework to the spin-dependent cross section. Together with the corresponding unpolarized calculation, these results enable consistent N$^3$LO predictions for longitudinal double-spin asymmetries and provide a precision baseline for future analyses of helicity PDFs and transverse-momentum-dependent helicity distributions.