Multiplicity dependence of quarkonia production at ultra high energies

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.