Multiplicity distribution of dipoles in QCD from Le, Mueller and Munier equation

TL;DR

This paper derives a QCD-based equation for the factorial moments of dipole multiplicity distribution, providing analytical results and a method for corrections to match experimental data.

Contribution

It introduces a QCD derivation of the factorial moments equation from the LMM framework and provides explicit solutions under the diffusion approximation.

Findings

Factorial moments follow a specific factorial form $M_k=k!N(N-1)^{k-1}$

The multiplicity distribution is a geometric-like distribution

A procedure for calculating corrections to the distribution is proposed.

Abstract

In this paper we derived in QCD the BFKL linear, inhomogeneous equation for the factorial moments of multiplicity distribution($M_k$) from LMM equation. In particular, the equation for the average multiplicity of the color-singlet dipoles($N$) turns out to be the homogeneous BFKL while $M_k \propto N^k$ at small $x$. Second, using the diffusion approximation for the BFKL kernel we show that the factorial moments are equal to: $M_k=k!N( N-1)^{k-1}$ which leads to the multiplicity distribution:$ \frac{\sigma_n}{\sigma_{in}}=\frac{1}{N} ( \frac{N\,-\,1}{N})^{n - 1}$. We also suggest a procedure for finding corrections to this multiplicity distribution which will be useful for descriptions of the experimental data.