The collectivity of transverse momentum fluctuations

TL;DR

The paper introduces $v_0(p_T)$ as a $p_T$-differential measure of event-by-event fluctuations in the mean transverse momentum, linking spectrum fluctuations to radial flow and collectivity. Using MUSIC hydrodynamics with fluctuating and smooth initial conditions for Pb+Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV, it shows that $v_0(p_T)/v_0$ is driven by temperature fluctuations and becomes largely independent of centrality and transport coefficients after scaling by $\langle p_T\rangle$, with a clear mass ordering for identified hadrons. The authors connect $v_0(p_T)$ to the ATLAS observation of the $p_T$-cut dependence of $\sigma_{p_T}$ by relating $v_0(p_T)/v_0= \delta \ln n(p_T)/\delta \ln [p_T]$ and demonstrate predictive power by reproducing multiple windows. The results provide a unified framework to characterize radial-flow fluctuations and motivate future studies in small systems and higher-$p_T$ regimes.

Abstract

We study the observable $v_0(p_T)$, which quantifies the relative change of $p_T$ spectra induced by event-by-event density fluctuations in the medium created in heavy-ion collisions. This quantity provides a direct measure of radial flow and serves as a probe of collectivity, complementing anisotropic flow coefficients. Using hydrodynamic model calculations, we predict the behavior of $v_0(p_T)$ and show that the scaled quantity $v_0(p_T)/v_0$ exhibits very little dependence on centrality and transport coefficients. We further find that the apparent influence of transport coefficients$-$particularly bulk viscosity$-$ on $v_0(p_T)$ largely originates from modifications of the event-averaged mean transverse momentum, $\langle p_T \rangle$. By expressing $v_0(p_T)/v_0$ as a function of $p_T/\langle p_T \rangle$, the genuine sensitivity of $v_0(p_T)$ to transport coefficients can be isolated. Moreover, since $v_0(p_T)$ is the $p_T$-differential measure of event-by-event $[p_T]$ fluctuations, it naturally explains the observed $p_T$-cut dependence of $σ_{p_T}$ measured by ATLAS collaboration.

Figures (3)

• Figure 1: Hydrodynamic model predictions of $v_0(p_T)/v_0$ for Pb+Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV are shown for charged particles in panel (a) and for identified particles in panel (b). In panel (a), the $x$-axis is scaled by $\langle p_T \rangle$. The smooth Initial Condition (IC) results are compared with those from fluctuating IC, as well as between two different impact parameters and for different transport coefficients. In panel (b), results for identified hadrons are shown using smooth IC at $b=0$ fm with $\eta/s=0.16$, with the focus on illustrating the mass hierarchy in $v_0(p_T)$.
• Figure 2: Symbols show the $N_{\text{ch}}$ dependence of $c_k = \sigma_{p_T}^2$ measured by the ATLAS Collaboration for different $p_T$ cuts in Pb+Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV ATLAS:2019pvn. Using the measured $c_k$ in one $p_T$ window as input (red), predictions for other $p_T$ windows are obtained with hydrodynamic model calculations of $v_0(p_T)$. The lines represent these model predictions.
• Figure 3: The ratio $\Delta p_T / \langle p_T \rangle$ is shown as a function of $\Delta N_{ch}/\langle N_{ch} \rangle$ for 0–1% central Pb+Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. Experimental data from the ATLAS Collaboration ATLAS:2024jvf are compared with our model predictions. We take the window $0.5<p_T<2$ (GeV/c) as input while predicted for the $0.5<p_T<5$ (GeV/c).