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Reciprocal symmetry and Koba-Nielsen-Olesen scaling violation in proton-proton collisions

Mustapha Ouchen* and Alex Prygarin†

  • *Contact author: mustapha.ouchen@ariel.ac.il
  • †Contact author: alexanderpr@ariel.ac.il
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Phys. Rev. D 114, 016004 – Published 6 July, 2026

DOI: https://doi.org/10.1103/11kp-cmgr

Abstract

We analyze the charged particle multiplicity distributions in p−p collisions and discuss the violation of the Koba-Nielsen-Olesen (KNO) scaling. We extract the deviations from the leading exponential behavior of the KNO scaled probability and identify a reciprocal symmetry z↔1/z in the KNO violating corrections observed in the ATLAS and CMS data at s=7,8,13  TeV. The symmetry imposes a local constraint on the multiplicity distribution at n=⟨n⟩, namely P′(⟨n⟩)=−P(⟨n⟩)/⟨n⟩, which we verify directly in the data. We use this constraint to extract the entanglement entropy from the well-measured region n≃⟨n⟩, avoiding the large uncertainties associated with the distribution tail.

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Phys. Rev. D 114, 016004– Published 6 July, 2026
  • Received 4 May 2026
  • Accepted 27 May 2026
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