Scaled transverse-momentum spectra as a probe of collective dynamics in heavy-ion collisions

Abstract

We investigate a scaling property of transverse-momentum spectra in ultrarelativistic heavy-ion collisions obtained by removing the global scales of multiplicity and mean transverse momentum. The resulting dimensionless observable isolates the intrinsic shape of the spectrum and reveals an approximate universality across collision centralities, systems, and energies. Hydrodynamic simulations reproduce this scaling on an event-by-event basis, indicating that it may originate from the collective dynamics of the quark-gluon plasma. Using Gaussian-process emulators trained on the JETSCAPE hybrid model, we perform a Bayesian analysis incorporating the scaled spectra as observables. The results demonstrate that the spectral shape provides independent constraints on key properties of the medium, including pre-equilibrium dynamics and initial-state granularity, while exposing tensions with parameter regions preferred by traditional $p_T$-integrated observables. We further explore an analogous scaling of transverse-mass spectra and observe a comparable universality across centralities and hadron species. These results suggest that scaled spectra provide a powerful new probe of collective dynamics and offer complementary constraints for the quantitative characterization of QCD matter created in heavy-ion collisions.

Figures (5)

• Figure 1: Prior (hatched gray bands) and posterior (orange and blue bands) model predictions for the scaled spectra $U(x_T)$ obtained with the Grad viscous correction, compared with ALICE Pb--Pb data at $\sqrt{s_{NN}} = 2.76~\mathrm{TeV}$ALICE:2013mez for centralities 0--5% and 50--60%. The narrow prior bands reflect the intrinsic universality of $U(x_T)$, while the posterior calibration sharpens these predictions, capturing the overall shape but revealing systematic deviations at low and high $x_T$. Experimental data points include combined uncorrelated statistical and systematic uncertainties. The original JETSCAPE posterior calibrated to $p_T$-integrated observables JETSCAPE:2020mzn are displayed by the orange bands. The scaled-spectra posterior, represented by the blue bands, is consistent with data but differs systematically from the integrated-observable posterior, indicating a tension between the two calibration strategies and highlighting the sensitivity of $U(x_T)$ to distinct regions of parameter space.
• Figure 2: Deviation from universal scaling for the scaled spectra $U(x_T)$ comparing the most central (0--5%) and most peripheral (50--60%) events. The curves labeled "Max" and "Min" represent the envelope of deviations obtained across the full model parameter space using the Grad viscous correction. The model predictions are compared with experimental measurements from ALICE ALICE:2013mez.
• Figure 3: First-order Sobol indices quantifying the contribution of each model parameter to deviations from universality in $U(x_T)$ for different centrality classes in Pb--Pb collisions at $\sqrt{s_{NN}} = 2.76~\mathrm{TeV}$. The analysis uses GP emulators trained on JETSCAPE simulations with the Grad viscous correction. The nucleon width $w$ dominates the breakdown of universality in peripheral collisions, while the free-streaming time $\tau_R$ and maximum bulk viscosity $(\zeta/s)_{\rm max}$ become more important in mid-central events.
• Figure 4: Scaled transverse-mass spectra for pions in Pb--Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV obtained from hydrodynamic simulations using the CE MAP parameters. Left: transverse-mass spectra for several centrality classes. Right: scaled spectra $U_{m_T}(x_{m_T})$ defined in Eq. \ref{['eq:scaled_mass_spectra']}, showing an approximate universality across centralities.
• Figure 5: Comparison of scaled spectra for different hadron species ($\pi$, $K$, $p$, $\Sigma$, $\Xi$) in the most central Pb--Pb collisions. Left: scaled transverse-momentum spectra $U(x_T)$. Right: scaled transverse-mass spectra Reduced transverse-mass spectra for the same hadron species $U_{m_T}(x_{m_T})$. The transverse-mass scaling shows a slightly stronger universality across hadron species.