Multiplicity of the doubly charmed state $T_{cc}^{+}$ in heavy-ion collisions

Abstract

We study the evolution of the doubly charmed state $T_{cc}^{+}$ in a hot hadron gas produced in the late stage of heavy-ion collisions. We use effective Lagrangians to calculate the thermally averaged cross sections of $T_{cc}^{+}$ production in reactions such as $D^{(\ast )}{D}^{(\ast )}\to T_{cc}^{+}\pi ,T_{cc}^{+}\rho$ and its absorption in the corresponding inverse processes. We then solve the rate equation to follow the time evolution of the $T_{cc}^{+}$ multiplicity, and determine how it is affected by the considered reactions during the expansion of the hadronic matter. We compare the evolution of the $T_{cc}^{+}$ abundance treated as a hadronic $S$-wave molecule and as a tetraquark state. Our results show that the tetraquark yield increases by a factor of about 2 at freeze-out, but it is still one order of magnitude smaller than the final yield of molecules formed from hadron coalescence. Also, the results indicate that $N_{T_{cc}}$ is more affected by interactions with hadronic medium than $N_{X(3872)}$ in similar conditions. We also show that yields depend very weakly on the system size, represented by $\mathcal{N}={\left[d{N}_{ch}/d\eta (\eta <0.5)\right]}^{1/3}$.

Comments: 10 pages; 6 figures; v2: added a new Section (Section IV) with a comprehensive study of the influence of the system size, represented by the density of charged particles measured at midrapidity $\mathcal{N}=\left[d{N}_{ch}/d\eta (\eta <0.5)\right]$, on the results