Mass-Dependent Non-Extensivity in Tsallis Blast-Wave Fits to Identified Hadron $p_T$ Spectra at RHIC and LHC

Abstract

We analyze identified-hadron transverse-momentum spectra from STAR Au+Au and ALICE Pb+Pb collisions over $\sqrt{s_{NN}} = 7.7$~GeV--$5.02$~TeV using an extended Tsallis Blast-Wave (TBW) framework, which includes a non-extensivity parameter $q$ to quantify the degree of incomplete thermal equilibrium. Conventionally, either a common value of $q$, or two separate $q$ values, one for mesons and one for baryons, are used to describe particle spectra in the TBW framework, with the latter being referred to as TBW4 in Ref.~\cite{Chen:2020zuw}. This work extends the TBW framework by studying the dependence of $q$ on different kinds of particles in detail. Fits allowing independent non-extensivity parameters $q$ for each species reveal a systematic correlation between $q$ and particle mass, except for quarkonia. Motivated by this trend, we introduce two new parameterizations: TBW5, which posits that $q$ depends linearly on particle mass, and TBW6, which allows the $q$ intercepts for mesons and baryons to differ. Across all energies and centralities considered in this study, TBW5 improves $χ^{2}/\mathrm{NDF}$ relative to the TBW4 fit in 71\% of the datasets, while TBW6 shows improvement in 94\% of the datasets. They perform especially well in central collisions. These results demonstrate a robust mass ordering in non-equilibrium behavior at kinetic freeze-out and provide a more accurate description of hadron spectra from RHIC to LHC energies.