Production of $ψ(4040)$, $ψ(4160)$, and $ψ(4415)$ mesons in strong interactions
Using the inelastic scattering of charmed strange mesons by open-charm mesons in hadronic matter produced in Pb-Pb collisions at the Large Hadron Collider, we study the production of $ψ(4040)$, $ψ(4160)$, and $ψ(4415)$ mesons. Master rate equations are established for inelastic scattering. The scattering is caused by quark interchange in association with color interactions between all constituent pairs in different mesons. We consider fifty-one reactions between charmed strange and open-charm mesons. Unpolarized cross sections for the reactions are obtained from a temperature-dependent interquark potential. The temperature dependence of the cross sections causes the contributions of the reactions to the production of $ψ(4040)$, $ψ(4160)$, and $ψ(4415)$ to change with decreasing temperature during the evolution of hadronic matter. For central Pb-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV, the master rate equations reveal that the $ψ(4040)$ number density is larger than the $ψ(4160)$ number density which is larger than the $ψ(4415)$ number density.