Orateur
Description
Quarkonium is considered as a probe, which may expose properties of the expanding QGP, produced in ultra-relativistic heavy-ion collisions. The theoretical description of the formation and the propagation of such a bound state of $c\bar c$ or $b\bar b$ quark-antiquark pairs is a challenging task.
Here we propose a model, which realizes quarkonium production in pp and AA collisions with help of quantal density matrices. This identification is embedded in a quantum-mechanical description of heavy quark propagation and interaction.
The Quarkonium production is realized in two steps:
1) The heavy quark production in pp collisions is given by the PYTHIA event generator;
2) The formation of a quarkonium from a $c\bar c$ or $b\bar b$ pair is described by the Wigner projection in momentum space with a spatial separation based on the uncertainty principle~\cite{Song:2017phm} . With this formalism we find a good agreement with the experimental rapidity and transverse momentum distributions for the ground states as well as for the excited states of $c\bar c$ and $b\bar b$ mesons in pp collisions from RHIC to LHC energies.
In a second step we test whether the quantal Remler formalism to describe bound state production in an expanding medium can be realized in a Monte Carlo approach for a QGP. For this study we use a box of thermalized QGP and investigate the time evolution of the c and $\bar c$, which are initially not in equilibrium with the QGP, either by localizing them in a smaller box and/or by giving them initially a different temperature. Comparing numerical and analytical results we demonstrate that, if there is no potential interaction between the c and $\bar c$, the original Remler formalism has to be modified by introducing a spatial diffusion rate to compensate for the expansion of the system~[1].
As a third step we study bottonium production in heavy-ion collisions, where the properties of bottonium in a QGP, the dissociation temperature and the temperature-dependant radius, are obtained by solving the Schr\"{o}dinger equation with the free energy from lattice QCD calculations as heavy quark potential. The elastic scattering of heavy (anti)quarks with light plasma partons is described by the dynamical quasi-particle model (DQPM). %It turns out that the bottonium is too much suppressed during the expansion as compared to the experimental results for Pb+Pb collisions at $\sqrt{s_{\rm NN}}=$ 5.02 TeV.
%To take into account the small size and color neutrality of bottomonium, we introduce a suppression of its scattering rate in a QGP to 10 \% of bottom and antibottom quarks.
%Such a suppression of the scattering rate brings the centrality dependence of the yields as well as the rapidity and transverse momentum distributions to a good agreement with the experimental findings~[2].
Considering that the two (anti)bottom quarks interact independently with QGP partons - as in the Remler formalism - and underestimate bottomonium yield, color neutrality has to be taken into account for agreement with the experimental results~[3].
[1] T.~Song, J.~Aichelin and E.~Bratkovskaya, Phys. Rev. C 96, no.1, 014907 (2017).
[2] T.~Song, J.~Aichelin and E.~Bratkovskaya, Phys. Rev. C 107, no.5, 054906 (2023).
[3] T.~Song, J.~Aichelin, J.~Zhao, P.~B.~Gossiaux and E.~Bratkovskaya,
Phys. Rev. C 108, no.5, 054908 (2023).
