Multiplicity of the doubly charmed state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:math> in heavy-ion collisions
Luciano M. Abreu, H. P. L. Vieira, F. S. Navarra
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 ${D}^{(*)}{D}^{(*)}\ensuremath{\rightarrow}{T}_{cc}^{+}\ensuremath{\pi},{T}_{cc}^{+}\ensuremath{\rho}$ 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 almost 2 orders of magnitude smaller than the final yield of molecules formed from hadron coalescence. We also analyze the dependence of the yields with the system size, represented by $\mathcal{N}={[d{N}_{ch}/d\ensuremath{\eta}(\ensuremath{\eta}<0.5)]}^{1/3}$. We make predictions that can be confronted with data, when they are available.