Scientists analyzed how different kinds of particles fly out of the fireball created in heavy-ion collisions. They used data from STAR (Au+Au collisions) and ALICE (Pb+Pb collisions) spanning center‑of‑mass energies from 7.7 GeV to 5.02 TeV. By fitting the measured transverse momentum (pT) spectra with an extended Tsallis Blast‑Wave model, they found a clear trend: the model’s non‑equilibrium parameter q depends on the particle mass for almost all hadrons studied.

The Tsallis Blast‑Wave (TBW) model combines two ideas. The Blast‑Wave picture assumes the hot fireball is moving outward with a collective radial flow and that, locally, particles have thermal motion. The Tsallis part adds a single number q, called the non‑extensivity parameter, which measures departure from perfect thermal equilibrium. When q = 1 the distribution reduces to the usual thermal (Boltzmann) shape; values q > 1 give heavier tails in momentum that signal incomplete thermalization or other non‑thermal sources.

The researchers first let each particle species have its own independent q. That exercise revealed a systematic correlation between q and particle mass, with the notable exception of quarkonia (heavy bound states like J/ψ, which were excluded from the main analysis). Motivated by this trend, they tested two compact ways to assign q across species. TBW5 assumes q grows linearly with particle mass. TBW6 allows the linear relation to have different intercepts for mesons and baryons, so the two groups can shift relative to each other.

Comparing fits, TBW5 improved the fit quality relative to the earlier two‑q scheme (called TBW4) in 71% of the datasets. TBW6 did even better, improving fits in 94% of the datasets. The mass‑dependent parameterizations worked best for central collisions. The authors interpret these results as evidence for a robust mass ordering in non‑equilibrium effects at kinetic freeze‑out (the stage when particles’ momenta are fixed), and as a more accurate, compact way to describe hadron spectra from RHIC to LHC energies.