The $X(3872)$ to $ψ(2S)$ yield ratio in heavy-ion collisions
In this work we evaluate the $X(3872)$ to $ ψ(2S) $ yield ratio ($N_X/N_{ψ(2S)}$) in Pb Pb collisions, taking into account the interactions of the $ψ(2S) $ and $ X(3872)$ states with light mesons in the hadron gas formed at the late stages of these collisions. We employ an effective Lagrangian approach to estimate the thermally-averaged cross sections for the production and absorption of the $ψ(2S)$ and use them in the rate equation to determine the time evolution of $N_{ψ(2S)}$. The multiplicity of these states at the end of mixed phase is obtained from the coalescence model. The multiplicity of $X(3872)$, treated as a bound state of $(D\bar D^{*} + c.c.)$ and also as a compact tetraquark, was already calculated in previous works. Knowing these yields, we derive predictions for the ratio ($N_X/N_{ψ(2S)}$) as a function of the centrality, of the center-of-mass energy and of the charged hadron multiplicity measured at midrapidity $[dN_{ch}/dη\,(η<0.5)]$. Finally, we make predictions for this ratio in Pb Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV to be measured by the ALICE Collaboration in the Run 3.