Multiplicity distribution and entropy of produced gluons in deep inelastic scattering at high energies

Eugene Levin

doi:10.1140/epjc/s10052-024-13008-w

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 662
https://doi.org/10.1140/epjc/s10052-024-13008-w

Regular Article - Theoretical Physics

Multiplicity distribution and entropy of produced gluons in deep inelastic scattering at high energies

Eugene Levin¹^,2^a

¹ Department of Particle Physics, Tel Aviv University, 69978, Tel Aviv, Israel
² Departemento de Física, Universidad Técnica Federico Santa María, and Centro Científico-Tecnológico de Valparaíso, Casilla 110-V, Avda. Espana 1680, Valparaiso, Chile

^a leving@tauex.tau.ac.il, eugeny.levin@usm.cl

Received: 3 July 2023
Accepted: 11 June 2024
Published online: 5 July 2024

Abstract

In this paper we found the multiplicity distribution of the produced gluons in deep inelastic scattering at large $z = ln (Q_{s}^{2} / Q^{2}) ≫ 1$ $z=\ln \left( Q^2_s/Q^2\right) \,\,\gg \,\,1$ where $Q_{s}$ $$ Q_s $$ is the saturation momentum and $Q^{2}$ $$Q^2$$ is the photon virtuality. It turns out that this distribution at large $n > \bar{n}$ $n > \bar{n}$ almost reproduces the KNO scaling behaviour with the average number of gluons $\bar{n} \propto exp (z^{2} / 2 κ)$ $\bar{n} \propto \exp \left( z^2/2 \kappa \right)$ , where $κ = 4.88$ $\kappa = 4.88$ in the leading order of perturbative QCD. The KNO function $Ψ (\frac{n}{\bar{n}}) = exp (- n / \bar{n})$ $\Psi \left( \frac{n}{\bar{n}}\right) = \exp \left( -\,n/\bar{n}\right)$ . For $n < \bar{n}$ $n < \bar{n}$ we found that $σ_{n} \propto (z - \sqrt{2 κ ln (n - 1)}) / (n - 1)$ $\sigma _n \propto \Big ( z - \sqrt{2 \,\kappa \,\ln (n-1)}\Big )/(n-1)$ . Such small n determine the value of entropy of produced gluons $S_{E} = 0.3 z^{2} / (2 κ)$ $S_E = 0.3\, z^2/(2\,\kappa )$ at large z. The factor 0.3 stems from the non-perturbative corrections that provide the correct behaviour of the saturation momentum at large b.

© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.