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Koba-Nielsen-Olesen scaling in quark and gluon jets at the LHC

Xiang-Pan Duan1,2,3,*, Lin Chen3,†, Guo-Liang Ma1,2,‡, Carlos A. Salgado3,§, and Bin Wu3,∥

  • 1Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of Modern Physics, Fudan University, Shanghai 200433, China
  • 2Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University, Shanghai 200438, China
  • 3Instituto Galego de Física de Altas Enerxías IGFAE, Universidade de Santiago de Compostela, E-15782 Galicia, Spain

  • *Contact author: xpduan20@fudan.edu.cn
  • †Contact author: lin.chen@usc.es
  • ‡Contact author: glma@fudan.edu.cn
  • §Contact author: carlos.salgado@usc.es
  • ∥Contact author: b.wu@cern.ch
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Phys. Rev. D 112, 094022 – Published 12 November, 2025

DOI: https://doi.org/10.1103/kz47-cv2q

Abstract

The Koba-Nielsen-Olesen (KNO) scaling of hadron multiplicity distributions, empirically confirmed to hold approximately in e+e− collisions and deep inelastic scattering, has been observed to be violated in hadron-hadron collisions. In this work, we show that the universality of KNO scaling can be extended to hadron-hadron collisions when restricted to QCD jets. We present a comprehensive study of KNO scaling in QCD jets produced in proton-proton collisions at the LHC. Using perturbative QCD calculations in the double logarithmic approximation and pythia simulations, we find that KNO scaling approximately holds for both quark and gluon jets across a broad jet pT range, from 0.1 to 2.5 TeV, at both the parton and hadron levels. Especially, we highlight characteristic differences between the KNO scaling functions of quark and gluon jets, with the quark-jet scaling function lying above that of gluon jets at both low and high multiplicities. This distinction is essential for interpreting inclusive jet data at the LHC. Furthermore, we propose direct experimental tests of KNO scaling in QCD jets at the LHC through quark-gluon discrimination using jet substructure techniques, as demonstrated by applying energy correlation functions to pythia-generated data.

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Phys. Rev. D 112, 094022– Published 12 November, 2025
  • Received 10 April 2025
  • Accepted 22 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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