Non-extensive statistical distributions of charmed meson production in Pb-Pb and pp($\overline{\text{p}}$) collisions

The mid-rapidity transverse-momentum spectra of charmed meson in Pb-Pb and pp($\overline{\text{p}}$) collisions are analyzed by Tsallis-Pareto distribution derived from non-extensive statistics. We perform uniform descriptions for both small and large systems over a wide range of collision energy and hadron transverse momentum. By establishing the relation between the event multiplicity and the Tsallis parameters, we observe that there is significant linearity between thermal temperature and Tsallis-q parameter in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV and 5.02 TeV. And the slope of the T $-$ (q - 1) parameter is positively correlated with the hadron mass. In addition, the charm mesons have higher thermal temperature than the light hadrons at the same q - 1, indicating that charmed flavor requires a higher temperature to achieve the same degree of non-extensive as light flavors in the heavy-ion collision. The same fit is performed to the transverse momentum spectra of charmed meson in pp($\overline{\text{p}}$) collision over a large energy range with Tsallis-Pareto distribution. It is found that the thermal temperature increases with system energy while the q parameter shows a saturated trend and stops at pp($\overline{\text{p}}$) limit, q - 1 = 0.142 $\pm$ 0.010. Meanwhile, the results of most peripheral Pb-Pb collisions are found to approach the pp($\overline{\text{p}}$) limit, which suggests that less medium effect and more in similarity with pp($\overline{\text{p}}$) collisions are found in more peripheral heavy-ion collisions.