Kinematic and dynamical origins of mean-$p_T$ fluctuations in heavy-ion collisions

TL;DR

The paper addresses how event-by-event mean-$p_T$ fluctuations probe collective quark-gluon plasma dynamics beyond traditional observables. It employs a Bayesian-calibrated multistage hydrodynamic framework, implemented with explicit STAR and ALICE fluctuation definitions, to study centrality and beam-energy dependencies and to separate genuine dynamical effects from kinematic acceptance biases. The results show that $R_{p_T}$ is dominated by soft-region correlations tied to radial flow and initial-state granularity, with significant sensitivity to model ingredients and hadronic afterburners; importantly, a scaled-cut analysis reveals that part of the observed beam-energy trend arises from kinematic projection rather than changes in underlying dynamics. The work thus validates mean-$p_T$ fluctuations as an independent constraint on calibrated hydrodynamics for the QGP and highlights the necessity of acceptance-aware comparisons in BES and high-energy data analyses. These insights advance our ability to quantify radial-flow fluctuations and to use $p_T$-dependent observables to sharpen tests of QGP properties.

Abstract

Event-by-event fluctuations of the mean transverse momentum (mean-$p_T$) provide a sensitive probe of collective dynamics beyond single-particle spectra and anisotropic flow. In this study, we present a systematic comparison of mean-$p_T$ fluctuation measurements with calculations based on a Bayesian-calibrated multistage hydrodynamic framework. The experimental definitions employed by the STAR and ALICE Collaborations are implemented explicitly and found to yield consistent results within controlled limits. We study the centrality and beam-energy dependence of the observable, its sensitivity to key soft-sector ingredients, and the impact of the kinematic $p_T$ acceptance. By introducing scaled-$p_T$ cuts, we demonstrate that a part of the apparent energy dependence arises from kinematic projection effects, while the remaining trends reflect genuine collective dynamics. Our results establish mean-$p_T$ fluctuations as a nontrivial and independent validation of calibrated hydrodynamic descriptions of the quark--gluon plasma.

Figures (4)

• Figure 1: Centrality dependence of $\sqrt{C_m}/\langle p_T\rangle$ in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. Model calculations are shown for two different lower transverse-momentum cuts, $0.15<p_T<2$ GeV and $0.2<p_T<2$ GeV, illustrating the sensitivity of the integrated observable to the kinematic acceptance. Published STAR data for $0.2<p_T<2$ GeV are shown for comparison STAR:2019dow.
• Figure 2: Relative response of $R_{p_T}\!\equiv\!\sqrt{C_m}/\langle p_T\rangle$ to variations of model ingredients in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV. Results are shown as fractional deviations with respect to the baseline calculation that includes shear and bulk viscosity, finite nucleon size, and a hadronic afterburner. Two representative centrality classes, 30–40% and 50–60%, are shown. The model variants correspond to switching off bulk viscosity ("no bulk"), disabling the hadronic afterburner ("no afterburner"), ideal hydrodynamic evolution without viscosity ("ideal hydro"), and a reduced nucleon size ("smaller nucleon"). Error bars indicate statistical uncertainties from the finite event sample.
• Figure 3: Beam-energy dependence of $\sqrt{C_m}/\langle p_T\rangle$ for charged hadrons in 30--40% central collisions, comparing results obtained with experimental kinematic cuts (solid symbols) and with scaled $p_T$ cuts (open symbols). The experimental cut setup follows the published experimental acceptances: $0.2<p_T<2$ GeV at $\sqrt{s_{NN}}=200$ GeV (STAR) and $0.15<p_T<2$ GeV at $\sqrt{s_{NN}}=2.76$ and $5.02$ TeV (ALICE). The scaled-cut results use energy-dependent windows defined relative to the charged-particle mean transverse momentum and anchored to the STAR acceptance at 200 GeV, yielding $0.226<p_T<2.264$ GeV at 2.76 TeV and $0.236<p_T<2.360$ GeV at 5.02 TeV.
• Figure 4: Species dependence of $\sqrt{C_m}/\langle p_T\rangle$ for identified $\pi^{\pm}$, $K^{\pm}$, and $p/\bar{p}$ in central (0--5%) Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV, evaluated in a common kinematic window $0.2<p_T<2$ GeV. The shaded band and dashed line indicate the corresponding result for inclusive charged hadrons in the same centrality and acceptance.