Transport of $D^0$ meson in hadronic matter in the domain of Non-Extensive statistics

Abstract

In this work, we investigate the drag and diffusion coefficients of $D^0$ meson propagating through a hadronic thermal bath by employing the Fokker Planck equation within the framework of Tsallis non extensive statistics. The non extensive parameter, $q$ accounts for the deviation from equilibrium and provides a more realistic description of the medium that is not perfectly thermalized. The hadronic bath, consisting of various mesonic and baryonic species, is characterized by different mass cutoffs that control the spectral composition of the medium. Our analysis shows that both the drag, $F$ and momentum diffusion coefficients, $\Gamma$ increases with temperature and also increases with increasing $q$ and mass cutoff. The spatial diffusion coefficient, $D_x$ exhibits a decreasing trend with temperature $T$, $q$ and mass cutoff which highlights the significant influence of non-equilibrium effects and hadronic composition on the transport behaviour of $D^0$ meson, offering valuable insights into the thermal and dynamical properties of the hadronic phase in heavy ion collisions. In this study while calculating the spatial diffusion coefficient, $D_x$ we observe that beyond $q$ = 1.24, $D_x$ goes below to the lower limit proposed in Ads/CFT theory. This suggests that 1.24 is the upper limit of non extensive parameter, $q$.