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  • Open Access

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

Liang Dong1,*, Shen Fang2,†, Jun Gao1,‡, Hai Tao Li3,§, Ding Yu Shao2,4,5,6,∥, and Yu Jiao Zhu7,¶

  • 1State Key Laboratory of Dark Matter Physics, Shanghai Key Laboratory for Particle Physics and Cosmology, Key Laboratory for Particle Astrophysics and Cosmology (MOE), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
  • 2Department of Physics, Center for Field Theory and Particle Physics, and Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Fudan University, Shanghai 200433, China
  • 3School of Physics, Shandong University, Jinan, Shandong 250100, China
  • 4Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University, Shanghai 200438, China
  • 5Center for High Energy Physics, Peking University, Beijing 100871, China
  • 6Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, Huizhou 516000, Guangdong Province, China
  • 7Max-Planck-Institut fur Physik, Werner-Heisenberg-Institut, Boltzmannstrasse 8, 85748 Garching, Germany

  • *Contact author: liang.dong@sjtu.edu.cn
  • †Contact author: sfang23@m.fudan.edu.cn
  • ‡Contact author: jung49@sjtu.edu.cn
  • §Contact author: haitao.li@sdu.edu.cn
  • ∥Contact author: dyshao@fudan.edu.cn
  • Contact author: yzhu@mpp.mpg.de
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Phys. Rev. Lett. 137, 081902 – Published 21 August, 2026

DOI: https://doi.org/10.1103/bf1g-9hq7

Abstract

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 qT-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(αs3) 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.

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Phys. Rev. Lett. 137, 081902– Published 21 August, 2026
  • Received 11 March 2026
  • Revised 22 June 2026
  • Accepted 28 July 2026
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