How the hadron gas affects X(3872) and ψ(2S) production in heavy ion collisions

Instituto de Física, Universidade de São Paulo, Rua do Matão, 1371, CEP 05508-090, São Paulo, SP, Brazil

^* e-mail: luciano.abreu@ufba.br
^** e-mail: navarra@if.usp.br
^*** e-mail: hildeson.paulo@ufba.br

Published online: 10 December 2024

Abstract

The X(3872) to ψ(2S) yield ratio (N_X/N_ψ(2S)) has been recently measured in pp, pPb and PbPb collisions by the LHCb and CMS Collaborations at the LHC. It was found that this ratio grows with the system size and this growth was attributed to the formation of quark gluon plasma and/or of a hot hadron gas. Here we focus on the effects of the hadron gas on the abundance of X(3872) and ψ(2S). The interaction of charmonium states with the light mesons in the gas can be studied with an effective Lagrangian formalism. One can calculate the relevant cross sections and use them as input in rate equations. With this formalism one can follow the time evolution of the X(3872) and ψ(2S) abundances until the final freeze-out of the gas. The initial conditions for this evolution are given by the coalescence model, which depends on the spatial configuration of the states and yields quite different numbers for compact tetraquarks and extended meson molecules. It has been found that the interactions in the hadron gas yield a suppression in most of the states and, most importantly, preserve the difference between the number of tetraquarks and the number of meson molecules, formed at the beginning of the hadronization. We discuss the predictions made for the ratio N_X/N_ψ(2S) in PbPb collisions at √s_NN = 5.02 TeV to be measured by the ALICE Collaboration in the Run 3. The existing calculations suggest that the molecular configuration generates a ratio compatible with the CMS data, whereas the ratio obtained with the tetraquark configuration is 50 times smaller.