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In this work we evaluate the $X(3872)$ to $ \psi (2S) $ yield ratio($N_X/N_{\psi(2S)}$) in Pb Pb collisions, taking into account the interactionsof the $\psi (2S) $ and $ X(3872)$ states with light mesons in the hadron gasformed at the late stages of these collisions. We employ an effectiveLagrangian approach to estimate the thermally-averaged cross sections for theproduction and absorption of the $\psi(2S)$ and use them in the rate equationto determine the time evolution of $N_{\psi(2S)}$. The multiplicity of thesestates at the end of mixed phase is obtained from the coalescence model. Themultiplicity 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 ($N_X/N_{\psi(2S)}$)as a function of the centrality, of the center-of-mass energy and of thecharged hadron multiplicity measured at midrapidity $[dN_{ch}/d\eta\,(\eta<0.5)]$. Finally, we make predictions for this ratio in Pb Pb collisionsat $\sqrt{s_{NN}} = 5.02$ TeV to be measured by the ALICE Collaboration in theRun 3.

The $X(3872)$ to $\psi (2S)$ yield ratio in heavy-ion collisions