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Multiplicity distribution of produced gluons in deep inelastic scattering: Main equations and their homotopy solutions for heavy nuclei

Carlos Contreras1,*, José Garrido1,2,†, and Eugene Levin3,‡

  • *Contact author: carlos.contreras@usm.cl
  • †Contact author: jose.garridom@sansano.usm.cl
  • ‡Contact author: leving@tauex.tau.ac.il
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Phys. Rev. D 113, 114021 – Published 11 June, 2026

DOI: https://doi.org/10.1103/ypc9-j9by

Abstract

In this paper we discuss the multiplicity distribution in the deep inelastic processes in the frame work of high energy QCD. We obtained three results. First, we get the new derivation of the equations for the cross sections of productions of n-cut Pomerons in the final states (σn). These equations coincide with the equations that have been derived using the Abramovsky-Gribov-Kancheli cutting rules but based on the dipole approach to QCD. Second, we developed the homotopy approach for finding the solutions to these equations. It consists with the analytic solution for the first iteration and the converge procedure of calculating the next iterations using computing. Third, we found the analytical solution for σn at large n≳N(z)=2N0zexp(z2/(2κ)) with z=ln(r2Qs2). Using this solution we calculate the entropy of the produced gluons at large z: SE=ln(N(z)), where the saturation momentum Qs and all constants are discussed in the text.

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Phys. Rev. D 113, 114021– Published 11 June, 2026
  • Received 4 April 2026
  • Accepted 13 May 2026
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