Sensitivity of p_T Fluctuations to the QCD Equation of State

We construct a novel theoretical baseline for dynamical transverse momentum correlations, $C_{pT}$, across a wide range of collision energies spanning the RHIC Beam Energy Scan (BES) program. For the first time, a unified framework is developed to describe the energy and centrality dependence of $C_{p_{\rm T}}$ from $\sqrt{s_{\text{NN}}} = 3.0$ to $200$~GeV. A central feature of this study is the implementation of Equation of State (EOS) inputs derived from Lattice QCD results at finite baryochemical potential $μ_{\rm B}$, representing the first such application to the measured transverse momentum correlations. Despite the minimalist nature of the fluid-dynamic evolution employed, the model effectively captures the characteristic centrality scaling of the experimental data. Our results indicate that while the bulk evolution is largely governed by the EOS and system lifetime at lower energies, significant deviations in peripheral collisions at top energies highlight the onset of non-thermal correlation mechanisms. This baseline provides a necessary benchmark for interpreting transverse momentum fluctuations in heavy-ion collisions and can aid in the search for the QCD critical point.