Multiplicity dependence of quarkonia production at ultra high energies

TL;DR

The paper develops a unitary-based framework for inclusive quarkonia production at ultra-high energies, combining $t$-channel unitarity, dipole densities from summed Pomeron loops, and the BFKL Pomeron calculus with AGK cutting rules. It applies this approach to the three-gluon fusion mechanism for $J/Ψ$ production and derives multiplicity distributions for produced gluons and quarkonia across different scattering systems in a zero-transverse-dimension setting, revealing a universal $KNO$-scaling structure. A key finding is that the ratio of the quarkonia to gluon multiplicity distributions scales as $rac{\mathcal{P}^{J/Ψ}_n}{\mathcal{P}^{gluon}_n}=\frac{n^2}{N(z)}$, indicating a quadratic enhancement with event multiplicity. The work provides a concrete method (Eq. MDJ3) to compute inclusive cross sections and multiplicity distributions, showing cancellations of multi-ladder contributions and offering predictions testable at high-energy colliders, with plans to extend to fixed transverse momentum observables.

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/Ψ}_n$) and without ($\mathcal{P}^{gluon}_n$) the quarkonia production. It turns out that $ \frac{\mathcal{P}^{J/Ψ}_n}{\mathcal{P}^{gluon}_n} \propto n^2 $ as has been expected and discussed in corresponding publications.

Figures (5)

• Figure 1: The production of quarkonia from $n$ parton cascades.
• Figure 2: Fig. \ref{['3p']}-a: The three gluon fusion mechanism of $J/\Psi$ production.Fig. \ref{['3p']}-b: the Mueller diagramMUDIA for $J/\Psi$ production, which illustrates the inter-relation between three gluon fusion and the triple BFKL Pomeron interaction. The wavy lines describe the BFKL Pomerons, while the helical curves represent gluons.
• Figure 3: Summing large Pomeron loops for dipole-dipole scattering. The wavy lines denote the BFKL Pomeron exchanges. The circles denote the amplitude $\gamma$ in the Born approximation of perturbative QCD.
• Figure 4: The cross-section corresponding to the first diagram of the Fig. \ref{['3p']}-a in the BFKL Pomeron calculus.The vertical wavy lines of different colors and shape passing through unitarity cut are BFKL Pomerons (described by the Green functions $G_{{I\!\!P}}\left( Y_{J/\Psi}, r\right)$ or $G_{{I\!\!P}}\left( Y_{J/\Psi}, r' \right)$ i n Eq. (\ref{['FD11']}))), helical lines correspond to the gluons.
• Figure 5: Fig. \ref{['mpsipsi']}: Summing large Pomeron loops for $J/\Psi$ production in dipole-dipole scattering. The wavy lines denote the BFKL Pomeron exchanges. The circles denote the amplitude $\gamma$ in the Born approximation of perturbative QCD. The blue blob denoted the $J/\Psi$ production due to three gluons fusion. The wavy lines with the cross indicate the cut Pomerons. The dashed lines denote the rapidity window, where the multiplicity of produced gluons is measured. The picture reflects the Mueller diagram technique for inclusive production (see Ref.MUDIA).