Influence of Non-extensivity on the drag and diffusion coefficients of hadronic matter

TL;DR

The paper investigates how non-equilibrium hadronic matter affects transport properties of propagating hadrons by solving the 3D Fokker–Planck equation within Tsallis nonextensive statistics. Drag $F$, momentum diffusion $oldsymbol{ abla}$, and spatial diffusion $D_x$ are derived as functions of temperature $T$, nonextensive parameter $q$, and the hadronic mass spectrum, linked through $oldsymbol{ abla}=...$, $ au^{-1}=F$, and $ au^{-1}=FmT$, with $D_x=rac{T}{mF}$. Results show $F$ and $oldsymbol{ abla}$ rise exponentially with $T$ and with $q$ and mass cutoffs, while $D_x$ decreases, indicating stronger coupling and reduced mobility; heavy mesons such as $D_0$, $J/ ext{ψ}$, and $Υ$ relax more slowly as their mass increases. These findings highlight the role of non-equilibrium effects and hadronic composition in shaping transport during the hadronic phase preceding freezeout in relativistic heavy-ion collisions. The framework provides a quantitative link between medium non-thermality, spectral content, and heavy-quark transport, informing models of energy loss and diffusion near the QCD transition.

Abstract

In this work, we investigate the drag and diffusion coefficients of various hadrons propagating through a hadronic thermal bath by employing the Fokker Planck equation within the framework of Tsallis nonextensive statistics. The nonextensive 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 $Γ$ increases exponentially with temperature and increases systematically 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 nonequilibrium effects and hadronic composition on the transport behaviour of hadrons, offering valuable insights into the thermal and dynamical properties of the hadronic phase preceding freezeout in heavy ion collisions. Additionally, we have studied the relaxation time of heavy mesons such as $D_0$, $J/ψ$ and $Υ$. We found that the heavier mesons relaxed later in comparison to the lighter mesons in the hadronic medium.

Figures (5)

• Figure 1: Variation of Drag coefficient of hadron gas as a function of temperature for various q values and mass cutoffs.
• Figure 2: Variation of Drag coefficient of heavy mesons as a function of temperature for various mass cutoffs.
• Figure 3: Relaxation times of $D_0$, $J/\psi$ and $\Upsilon$ and their ratios.
• Figure 4: Variation of Momentum Diffusion coefficient of $D_0$ meson with temperature for various q values and mass cutoffs.
• Figure 5: Variation of Spatial Diffusion coefficient with temperature of $D_0$ meson.