X(3872) to ψ(2S) yield ratio in heavy-ion collisions

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 interactions of the psi(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 psi(2S) and use them in the rate equation to determine the time evolution of N-psi(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 (DD<overline>& lowast;+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 the charged hadron multiplicity measured at midrapidity [dNch/d eta(eta<0.5)]. Finally, we make predictions for this ratio in Pb Pb collisions at root sNN(-)=5.02 TeV to be measured by the ALICE Collaboration in the Run 3. Our findings suggest that the molecular configuration generates aratio compatible with the data, whereas the ratio obtained with the tetraquark configuration is 50 timessmaller.