Next-to-Next-to-Leading-Order QCD Corrections to Hadron Production in Deep-Inelastic Scattering at Finite Transverse Momentum.

We present the first 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 O(α_{s}^{3}) corrections. Our NNLO results generally demonstrate an improved convergence of the perturbative expansion and a reduction in scale uncertainties compared to previous next-to-leading order ones, especially for comparisons to multiplicity data from the ZEUS Collaboration. This Letter 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.