Breaking of factorization of two-particle correlations in hydrodynamics

Abstract

The system formed in ultrarelativistic heavy-ion collisions behaves as a nearly-perfect fluid. This collective behavior is probed experimentally by two-particle azimuthal correlations, which are typically averaged over the properties of one particle in each pair. In this Letter, we argue that much additional information is contained in the detailed structure of the correlation. In particular, the correlation matrix exhibits an approximate factorization in transverse momentum, which is taken as a strong evidence for the hydrodynamic picture, while deviations from the factorized form are taken as a signal of intrinsic, "nonflow" correlations. We show that hydrodynamics in fact predicts factorization breaking as a natural consequence of initial state fluctuations and averaging over events. We derive the general inequality relations that hold if flow dominates, and which are saturated if the matrix factorizes. For transverse momenta up to 5 GeV, these inequalities are satisfied in data, but not saturated. We find factorization breaking in event-by-event ideal hydrodynamic calculations that is at least as large as in data, and argue that this phenomenon opens a new window on the study of initial fluctuations.

Anisotropic flow of identified particles in Pb–Pb collisions at √sNN= 2.76 TeV measured with ALICE at the LHC

“…At LHC energies pion and kaon v 2 is slightly above the RHIC results, while anti-proton v 2 shows the effect of the stronger radial flow, as expected from hydrodynamical model calculations [7][8][9]. Recent hydrodynamic simulations [14,15] predict that the flow angle and the fluctuations may affect in a different way particles with different p T . In order to verify it a new observable can be defined v 2 [2] which is the flow coefficent obtained using a sample of reference particles selected in the same p T interval of the particles under investigation [13].…”

Initial state fluctuations and final state correlations in relativistic heavy-ion collisions

“…(34), which is usually separated as the traceless (shear) and scalar (bulk) part. Each conserved current has an associated thermodynamic chemical potential µ i , related to the charged density ρ i and temperature T by a thermodynamic relation, and all of these coefficients can depend on, e.g., the local energy and charge densities.…”

“…One of the most common is the two-particle cumulant flow measurement v n {2}, which restricts only one particle of the pair to a narrow region in transverse momentum and/or pseudorapidity (and often a particular identified particle species), while the second particle in each pair is an unidentified hadron that is allowed to be taken from a wide range in phase space. This correlation is then divided by the square root of a fully integrated correlation to obtain [32,33,34] …”

Azimuthal anisotropies and initial-state fluctuations from SPS to LHC energies

“…The two-particle correlations between strange (K 0 S or Λ/Λ) and charged particles [13] also revealed similar ridge structures, and the extracted v 2 , scaled to the number of constituent quarks (n q ) shows that hydrodynamic behavior happens on the partonic level. It is shown in [14,15] that even if the hydrodynamics is the only source of the long-range correlations, the initialstate fluctuations makes the event plane angle, Ψ n , dependent on both, p T and η. This leads to factorization breaking of the V nΔ into a product of single-particle anisotropies v n [16].…”