A new probe of radial flow

The ATLAS and ALICE collaborations have announced the first results of a new way to measure the “radial flow” of quark–gluon plasma (QGP). The two analyses offer a fresh perspective into the fluid-like behaviour of QCD matter under extreme conditions, such as those that prevailed after the Big Bang. The measurements are highly complementary, with ALICE drawing on their detector’s particle-identification capabilities and ATLAS leveraging the experiment’s large rapidity coverage.

At the Large Hadron Collider, lead–ion collisions produce matter at temperatures and densities so high that quarks and gluons momentarily escape their confinement within hadrons. The resulting QGP is believed to have filled the universe during its first few microseconds, before cooling and fragmenting into mesons and baryons. In the laboratory, these streams of particles allow researchers to reconstruct the dynamical evolution of the QGP, which has long been known to transform anisotropies of the initial collision geometry into anisotropic momentum distributions of the final-state particles.

Compelling evidence

Differential measurements of the azimuthal distributions of produced particles over the last decades have provided compelling evidence that the outgoing momentum distribution reflects a collective response driven by initial pressure gradients. The isotropic expansion component, typically referred to as radial flow, has instead been inferred from the slope of particle spectra (see figure 1). Despite its fundamental role in driving the QGP fireball, radial flow lacked a differential probe comparable to those of its anisotropic counterparts.

That situation has now changed. The ALICE and ATLAS collaborations recently employed the novel observable v₀(p_T) to investigate radial flow directly. Their independent results demonstrate, for the first time, that the isotropic expansion of the QGP in heavy-ion collisions exhibits clear signatures of collective behaviour. The isotropic expansion of the QGP and its azimuthal modulations ultimately depend on the hydrodynamic properties of the QGP, such as shear or bulk viscosity, and can thus be measured to constrain them.

Traditionally, radial flow has been inferred from the slope of p_T-spectra, with the p_T-integrated radial-flow extracted via fits to “blast wave” models. The newly introduced differential observable v₀(p_T) captures fluctuations in spectral shape across p_T bins. v₀(p_T) retains differential sensitivity, since it is defined as the correlation (technically the normalised covariance) between the fraction of particles in a given p_T-interval and the mean transverse momentum of the collision products within a single event, [p_T]. Roughly speaking, a fluctuation raising [p_T] produces a positive v₀(p_T) at high p_T due to the fractional yield increasing; conversely, the fractional yield decreasing at low p_T causes a negative v₀(p_T). A pseudorapidity gap between the measurement of mean p_T and the particle yields is used to suppress short-range correlations and isolate the long-range, collective signal. Previous studies observed event-by-event fluctuations in [p_T], related to radial flow over a wide p_T range and quantified by the coefficient v₀^ref, but they could not establish whether these fluctuations were correlated across different p_T intervals – a crucial signature of collective behaviour.

Origins

The ATLAS collaboration performed a measurement of v₀(p_T) in the 0.5 to 10 GeV range, identifying three signatures of the collective origin of radial flow (see figure 2). First, correlations between the particle yield at fixed p_T and the event-wise mean [p_T] in a reference interval show that the two-particle radial flow factorises into single-particle coefficients as v₀(p_T) × v₀^ref for p_T < 4 GeV, independent of the reference choice (left panel). Second, the data display no dependence on the rapidity gap between correlated particles, suggesting a long-range effect intrinsic to the entire system (middle panel). Finally, the centrality dependence of the ratio v₀(p_T)/v₀^ref followed a consistent trend from head-on to peripheral collisions, effectively cancelling initial geometry effects and supporting the interpretation of a collective QGP response (right panel). At higher p_T, a decrease in v₀(p_T) and a splitting with respect to centrality suggest the onset of non-thermal effects such as jet quenching. This may reveal fluctuations in jet energy loss – an area warranting further investigation.

Using more than 80 million collisions at a centre-of-mass energy of 5.02 TeV, ALICE extracted v₀(p_T) for identified pions, kaons and protons across a broad range of centralities. ALICE observes v₀(p_T) to be negative at low p_T, reflecting the influence of mean-p_T fluctuations on the spectral shape (see figure 3). The data display a clear mass ordering at low p_T, from protons to kaons to pions, consistent with expectations from collective radial expansion. This mass ordering reflects the greater “push” heavier particles experience in the rapidly expanding medium. The picture changes above 3 GeV, where protons have larger v₀(p_T) values than pions and kaons, perhaps indicating the contribution of recombination processes in hadron production.

The results demonstrate that the isotropic expansion of the QGP in heavy-ion collisions exhibits clear signatures of collective behaviour

The two collaborations’ measurements of the new v₀(p_T) observable highlight its sensitivity to the bulk-transport properties of the QGP medium. Comparisons with hydrodynamic calculations show that v₀(p_T) varies with bulk viscosity and the speed of sound, but that it has a weaker dependence on shear viscosity. Hydrodynamic predictions reproduce the data well up to about 2 GeV, but diverge at higher momenta. The deviation of non-collective models like HIJING from the data underscores the dominance of final-state, hydrodynamic-like effects in shaping radial flow.

These results advance our understanding of one of the most extreme regimes of QCD matter, strengthening the case for the formation of a strongly interacting, radially expanding QGP medium in heavy-ion collisions. Differential measurements of radial flow offer a new tool to probe this fluid-like expansion in detail, establishing its collective origin and complementing decades of studies of anisotropic flow.