NNLO QCD corrections to hadron production in DIS at finite transverse momentum

Abstract

We present the first complete calculation of hadron production in deep-inelastic scattering (DIS) at finite transverse momentum to next-to-next-to-leading order (NNLO) in perturbative QCD. To overcome the long-standing challenge of infrared divergences in semi-inclusive processes with identified final state hadrons at finite transverse momentum, we implement the recently developed $q_T$-subtraction framework based on the recoil-free jet definition. By utilizing the winner-take-all recombination scheme, we achieve a consistent factorization for hadron-jet associated production, enabling the inclusion of $\mathcal{O}(\alpha_s^3)$ corrections. Our results demonstrate a significantly improved stabilization of the perturbative expansion and a reduction in scale uncertainties compared to previous next-to-leading order predictions. We find that the NNLO corrections are essential for a robust description of high precision multiplicity data from the ZEUS collaborations. This work provides a high precision theoretical foundation for the upcoming Electron-Ion Collider era and establishes a new benchmark for the exploration of the nucleon's three-dimensional structure.