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

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. We present a systematic study of mean-$p_T$ fluctuation observables using a Bayesian-calibrated multistage hydrodynamic framework, including quantitative comparisons to RHIC measurements and model-based investigations of beam-energy and kinematic-acceptance effects. 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.

💡 Research Summary

This paper investigates event‑by‑event fluctuations of the mean transverse momentum (mean‑pT) as a sensitive probe of collective dynamics in relativistic heavy‑ion collisions. Using a Bayesian‑calibrated multistage hydrodynamic framework implemented in the JETSCAPE suite, the authors simulate Au+Au collisions at √sNN = 200 GeV and Pb+Pb collisions at √sNN = 5.02 TeV. The model includes TRENTON initial conditions, a short free‑streaming pre‑equilibrium stage, second‑order viscous hydrodynamics with temperature‑dependent shear and bulk viscosities (MUSIC), Cooper–Frye particlization, and a hadronic afterburner (SMASH). The Maximum‑A‑Posteriori (MAP) parameter set from previous Bayesian analyses is used without further tuning, providing a genuine prediction for mean‑pT fluctuation observables that were not part of the original calibration.

Two experimental definitions of the fluctuation measure are implemented explicitly: the STAR prescription, which uses the ensemble‑averaged mean pT as a reference, and the ALICE prescription, which uses the event‑wise mean pT. By applying both definitions to the same simulated events, the authors demonstrate that the resulting values of the dimensionless observable RpT ≡ √Cm/⟨pT⟩ are practically identical for the large multiplicities and narrow centrality bins considered, confirming that the choice of reference does not bias the comparison.

The baseline comparison to STAR data shows that the model underestimates RpT when the standard experimental lower pT cut (0.2 GeV) is applied. Systematically lowering the cut to 0.15 GeV raises the simulated RpT and brings it into better agreement with the measurements, indicating that the fluctuation signal is dominated by very soft particles where radial flow effects are strongest. This sensitivity to the low‑pT region is further illustrated by an analytical expression for the covariance, which emphasizes the weight of low‑pT yields in the integrated observable.

A series of controlled model variations explores the sensitivity of RpT to specific physical ingredients. Turning off bulk viscosity produces only modest, centrality‑dependent changes, while removing all viscosities (ideal‑hydro limit) leads to a clear increase of RpT, especially in peripheral collisions, highlighting the role of shear‑induced damping of event‑by‑event radial flow fluctuations. Reducing the nucleon width in the initial condition from 1.12 fm to 0.8 fm yields the largest enhancement of RpT across centralities, underscoring the observable’s strong response to initial‑state granularity. Disabling the hadronic afterburner produces opposite trends in mid‑central versus peripheral events, reflecting a competition between correlation buildup during the hadronic phase and dilution effects from varying multiplicities.

Finally, the authors introduce scaled pT cuts to disentangle genuine energy‑dependent dynamics from kinematic projection effects. By scaling the lower and upper pT limits proportionally to the mean pT at each beam energy, they show that part of the apparent increase of RpT from RHIC to LHC energies can be attributed to the broader acceptance of low‑pT particles at higher energies. After correcting for this effect, the remaining trend reflects true changes in the QGP’s collective behavior, such as variations in viscosity or initial‑state fluctuations.

In summary, the study establishes mean‑pT fluctuations as a non‑trivial, independent validation of calibrated hydrodynamic models. The observable is highly sensitive to shear viscosity, initial‑state granularity, and the soft‑momentum sector, while being robust against the specific experimental definition used. These findings pave the way for future precision measurements of momentum‑space correlations and provide a new avenue to constrain the transport properties of the quark‑gluon plasma.