Multiplicity dependence of quarkonia production at ultra high energies

TL;DR

This paper presents a high-energy QCD approach to calculate inclusive quarkonia production at ultra high energies, focusing on the dependence of production on hadron multiplicity using a three-gluon fusion mechanism.

Contribution

It introduces a novel method based on t-channel unitarity and dipole densities to analyze quarkonia production without assuming saturation scale multiplicity dependence.

Findings

Quarkonia production multiplicity distribution scales as n^2.

The ratio of quarkonia to gluon multiplicity distributions is proportional to n^2.

The approach aligns with previous theoretical expectations.

Abstract

In this paper we propose an approach in high energy QCD, which allows us to calculate the inclusive quarkonia production at ultra high energies. This approach is based on $t$-channel unitarity and on the expressions for dipole densities from the procedure of summing of large Pomeron loops which we have developed in our previous papers. In the framework of this approach we discuss the dependence of quarkonia production on the multiplicity of the accompanying hadrons. In this paper we used the three gluons fusion mechanism for quarkonia production, without assuming the multiplicity dependence of the saturation scale. We found the multiplicity distribution of produced gluon with ( $ \mathcal{P}^{J/\Psi}_n$) and without ($\mathcal{P}^{gluon}_n$) the quarkonia production. It turns out that $ \frac{\mathcal{P}^{J/\Psi}_n}{\mathcal{P}^{gluon}_n} \propto n^2 $ as has been expected and discussed in corresponding publications.