This paper builds a simple, physics‑based baseline for dynamical transverse‑momentum correlations (CpT) measured in heavy‑ion collisions. The authors focus on event‑by‑event fluctuations of the mean transverse momentum ⟨pT⟩. Transverse momentum here means the particle momentum sideways to the beam. CpT is a way to quantify how much ⟨pT⟩ varies from collision to collision and how those variations are correlated across the collision zone.

The central idea is to describe how those correlations evolve as a hot, dense fireball expands and cools. The authors start from a linearized, relativistic fluid picture and derive a Langevin‑type equation for the two‑point correlator of transverse momentum density. That evolution combines three physical effects: dilution by the longitudinal expansion of the fireball (a Bjorken expansion), viscous diffusion driven by the shear viscosity, and stochastic thermal noise required by the fluctuation–dissipation theorem. The model is integrated from an initial proper time τ0 = 0.6 fm/c to a freeze‑out time taken from measurements of the longitudinal femtoscopic radius.

A key novelty is that the equation of state (EOS) inputs come from lattice quantum chromodynamics (QCD) calculations evaluated at finite baryon chemical potential μB. In plain language, the EOS tells how pressure, energy and other thermodynamic quantities relate in the hot matter; μB tracks how many more baryons than anti‑baryons are present. The authors also use lattice‑motivated values for the speed of sound and the shear viscosity over entropy ratio η/s as functions of temperature and μB. They then map the model output onto the experimental observable CpT over a wide collision‑energy range, √sNN = 3.0–200 GeV, and across centrality (how head‑on the collisions are).

The minimalist evolution captures an important feature seen in data: the characteristic centrality scaling of CpT across energies. According to the study, at lower collision energies the bulk evolution — driven by the EOS and a longer system lifetime — largely controls the CpT signal. At the highest energies and in peripheral (less central) collisions, the model finds significant deviations. The authors interpret these deviations as the appearance of non‑thermal correlation mechanisms that their thermal baseline does not include.