Production of ψ(4040) , ψ(4160) , and ψ(4415) mesons in hadronic matter

Abstract

We present the first study of production of $\ensuremath{\psi}(4040)$, $\ensuremath{\psi}(4160)$, and $\ensuremath{\psi}(4415)$ mesons in hadronic matter. Quark interchange between two colliding charmed mesons leads to the production of the three mesons. We calculate unpolarized cross sections for the reactions $D\overline{D}\ensuremath{\rightarrow}\ensuremath{\rho}R$, $D{\overline{D}}^{*}\ensuremath{\rightarrow}\ensuremath{\pi}R$, $D{\overline{D}}^{*}\ensuremath{\rightarrow}\ensuremath{\rho}R$, ${D}^{*}\overline{D}\ensuremath{\rightarrow}\ensuremath{\pi}R$, ${D}^{*}\overline{D}\ensuremath{\rightarrow}\ensuremath{\rho}R$, ${D}^{*}{\overline{D}}^{*}\ensuremath{\rightarrow}\ensuremath{\pi}R$, and ${D}^{*}{\overline{D}}^{*}\ensuremath{\rightarrow}\ensuremath{\rho}R$, where $R$ stands for $\ensuremath{\psi}(4040)$, $\ensuremath{\psi}(4160)$, and $\ensuremath{\psi}(4415)$. In the temperature region covering hadronic matter, the peak cross sections of producing $\ensuremath{\psi}(4040)$ are similar to or larger than the ones of producing $\ensuremath{\psi}(4415)$, and the latter are generally larger than those of producing $\ensuremath{\psi}(4160)$. With the cross sections, we establish new master rate equations for $\ensuremath{\psi}(4040)$, $\ensuremath{\psi}(4160)$, and $\ensuremath{\psi}(4415)$. The equations are solved for central Pb-Pb collisions at $\sqrt{{s}_{NN}}=5.02\text{ }\text{ }\mathrm{TeV}$ at the Large Hadron Collider. Solutions of the equations show that the $\ensuremath{\psi}(4040)$ number density at kinetic freeze-out of hadronic matter is larger than the $\ensuremath{\psi}(4415)$ number density, which is larger than the $\ensuremath{\psi}(4160)$ number density.