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<p>We revisit the calculation of the next-to-leading order (NLO) corrections to dijet production in electron-ion collisions at small <i>x</i>. We focus on the back-to-back configuration where the relative transverse momentum <i>P</i><sub>⊥</sub> of the measured jets is much larger than both their momentum imbalance <i>K</i><sub>⊥</sub> and the target saturation momentum <i>Q</i><sub><i>s</i></sub>(<i>x</i>, <i>A</i>). In this regime, we present for the first time a complete calculation of the real NLO corrections, associated with gluon emissions outside the jet cones, at leading power in 1/<i>P</i><sub>⊥</sub>. Our result exhibits TMD factorisation, with the same hard factor as at tree-level and a NLO correction to the Weiszäcker-Williams (WW) gluon transverse momentum dependent (TMD) distribution which involves four Wilson-line operators. By studying different kinematical regimes for <i>K</i><sub>⊥</sub> and for the radiated gluon, we recover all the quantum evolutions that were previously identified for this process at NLO: the B-JIMWLK high-energy evolution and the CSS evolution of the gluon WW TMD, and the DGLAP evolution of the gluon PDF. When both <i>K</i><sub>⊥</sub> and the transverse momentum transferred by the target are large compared to <i>Q</i><sub><i>s</i></sub>, all the Wilson-line operators boil down to the unintegrated gluon distribution and our NLO result for the gluon TMD can be used to isolate the transverse-momentum dependent gluon splitting function.</p>

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Gluon splitting at small x: a unified derivation for the JIMWLK, DGLAP and CSS equations

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  • 发表日期：

    2026年3月20日

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  • Paul Caucal,
  • Edmond Iancu,
  • Farid Salazar,
  • Feng Yuan

摘要

We revisit the calculation of the next-to-leading order (NLO) corrections to dijet production in electron-ion collisions at small x. We focus on the back-to-back configuration where the relative transverse momentum P⊥ of the measured jets is much larger than both their momentum imbalance K⊥ and the target saturation momentum Qs(x, A). In this regime, we present for the first time a complete calculation of the real NLO corrections, associated with gluon emissions outside the jet cones, at leading power in 1/P⊥. Our result exhibits TMD factorisation, with the same hard factor as at tree-level and a NLO correction to the Weiszäcker-Williams (WW) gluon transverse momentum dependent (TMD) distribution which involves four Wilson-line operators. By studying different kinematical regimes for K⊥ and for the radiated gluon, we recover all the quantum evolutions that were previously identified for this process at NLO: the B-JIMWLK high-energy evolution and the CSS evolution of the gluon WW TMD, and the DGLAP evolution of the gluon PDF. When both K⊥ and the transverse momentum transferred by the target are large compared to Qs, all the Wilson-line operators boil down to the unintegrated gluon distribution and our NLO result for the gluon TMD can be used to isolate the transverse-momentum dependent gluon splitting function.