The collectivity of transverse momentum fluctuations

TL;DR

This paper introduces and analyzes the observable $v_0(p_T)$ to measure radial flow and collectivity in heavy-ion collisions, highlighting its minimal dependence on centrality and transport coefficients, and its relation to $p_T$ fluctuations.

Contribution

It predicts the behavior of $v_0(p_T)$ using hydrodynamic models and isolates its genuine sensitivity to transport coefficients by normalizing with $ angle p_T angle$.

Findings

$v_0(p_T)/v_0$ shows little dependence on centrality and transport coefficients.

The influence of transport coefficients on $v_0(p_T)$ mainly stems from changes in $ angle p_T angle$.

Expressing $v_0(p_T)/v_0$ as a function of $p_T/ angle p_T angle$ isolates its sensitivity to transport coefficients.

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 $\sigma_{p_T}$ measured by ATLAS collaboration.