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  • Open Access

Next-to-Leading-Order QCD Corrections to Nucleon Dirac Form Factors

Long-Bin Chen1, Wen Chen2,3, Feng Feng4,5,*, Siwei Hu5,6, and Yu Jia5,6,†

  • *Contact author: f.feng@outlook.com
  • †Contact author: jiay@ihep.ac.cn
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Phys. Rev. Lett. 135, 131903 – Published 24 September, 2025

DOI: https://doi.org/10.1103/r25y-rsz5

Abstract

The leading-order perturbative QCD (pQCD) predictions for nucleon electromagnetic form factors were first made in late 1970s. In this Letter, for the first time, we accomplish the calculation of the next-to-leading-order (NLO) QCD corrections to nucleon Dirac form factors at large momentum transfer to leading-twist accuracy in the collinear factorization approach, specifically within the Krankl and Manashov renormalization scheme. The effect of NLO perturbative corrections turns out to be positive and substantial. Taking the nucleon leading-twist light-cone distribution amplitudes determined from the recent lattice simulations as input, we find that the state-of-the-art pQCD predictions significantly underestimate the available nucleon Dirac form factors in both spacelike and timelike domains. This nuisance indicates that some additional soft nonfactorizable contribution might be called for to account for the measured nucleon electromagnetic form factor data up to Q2≈30  GeV2.

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Phys. Rev. Lett. 135, 131903– Published 24 September, 2025
  • Received 15 August 2024
  • Revised 8 July 2025
  • Accepted 29 August 2025
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