Multiplicity of $Z_{cs}(3985)$ in heavy ion collisions

Using the coalescence model we compute the multiplicity of $Z_{cs} (3985)^-$ (treated as a compact tetraquark) at the end of the quark gluon plasma phase in heavy ion collisions. Then we study the time evolution of this state in the hot hadron gas phase. We calculate the thermal cross sections for the collisions of the $Z_{cs} (3985)^-$ with light mesons using effective Lagrangians and form factors derived from QCD sum rules for the vertices $Z_{cs}\bar{D}_{s }^* D$ and $Z_{cs} \bar{D}_{s} D^{*}$. We solve the kinetic equation and find how the $Z_{cs} (3985)^-$ multiplicity is affected by the considered reactions during the expansion of the hadronic matter. A comparison with the statistical hadronization model predictions is presented. Our results show that the tetraquark yield increases by a factor of about $2-3$ from the hadronization to the kinetic freeze-out. We also make predictions for the dependence of the $Z_{cs} (3985)^-$ yield on the centrality, the center-of-mass energy and the charged hadron multiplicity measured at midrapidity $\left[ d N_{ch} / d \eta (\eta < 0.5)\right]$.