Evolving charge correlations in a hybrid model with both hydrodynamics and hadronic Boltzmann descriptions

Background: Correlations from charge correlation, known as charge balance functions, provide critical tests of the chemical evolution of matter in a heavy-ion collision. Comparisons of experimental balance functions with calculations from parametric descriptions of the final state suggest that the charge production in the earliest stages of a heavy-ion collision are consistent with having generated an amount of light up, down, and strange quarks that are largely consistent with expectations for creating a chemically equilibrate quark-gluon plasma.

Purpose: This work describes a full simulation of the evolving correlations superimposed on a state-of-the-art microscopic description of the collision.

Methods: The creation and diffusion of balancing charges is modeled on the background of a hybrid description of the evolution based on hydrodynamics, for when the matter's temperature is above 155 MeV, and a microscopic hadronic simulation, for the breakup stage. The translation of the charge-charge correlation function, indexed by the flavors up, down, and strange, into correlations between specific hadron species is built on the assumption that differential charges enhance differential yields according to statistical equilibrium. Monte Carlo methods are implemented when applicable.

Results: The charge balance functions are predicted for pairs indexed by charge alone or by whether the particle pairs are any combination of pions, kaons, or protons. Comparisons with experiment are remarkably successful except for the proton-kaon balance functions.

Conclusions: This demonstrates first that two-particle correlations from charge conservation can be calculated for a state-of-the-art model of the evolution with moderate amounts of computation. Aside from the magnitude of the proton-kaon correlations, the calculations well describe preliminary experimental results from the STAR Collaboration at the Relativistic Heavy Ion Collider. Ignoring the one disagreement, this suggests that the matter in a heavy-ion collision comes close to maintaining chemical equilibrium during the superhadronic stage of a heavy-ion collision.

Figure 1

[(a)–(f)] Charge balance functions for unidentified charged particles binned by relative pseudorapidity for six different centralities from 0–5% to 50–60%. The model (solid blue lines) approximately reproduces the narrowing of the experimental balance functions (stars) with increasing centrality. [(g)–(l)] The same as (a)–(f) but binned by relative azimuthal angle. The larger volumes for more-central collisions make it more difficult for charges to diffuse to regions with different radial flow, hence the balance functions are narrower. The contributions from the hydrodynamic correlations (green dashed lines) and from the correlations that originated in the cascade (green dotted lines) are of similar strength, with the cascade contribution being narrower. Oscillations of the experimental balance functions for the most-central collisions in panels (k) and (l) are likely from the sector boundaries of the STAR experiment. Some of the deviations for small $\mathrm{\Delta }\eta$ and $\mathrm{\Delta }\varphi$ might be due to femtoscopic correlations.

Figure 2

Balance functions, indexed by hadronic species and binned by relative rapidity, are shown for central (0–5%) Au+Au collisions at ${\sqrt{s}}_{NN}=200$ GeV. The model calculations (green lines) are compared to preliminary measurements from the STAR Collaboration at RHIC [7] (red stars). Matching the relatively broader structure of the $K^{+}{K}^{-}$ and $p\overline{p}$ balance functions relative to the ${\pi }^{+}\pi +-$ balance function provides compelling evidence that the a chemically equilibrated quark-gluon plasma was created. Unfortunately, such conclusions are tempered by the failure of the model to reproduce the $p{K}^{-}$ experimental balance functions.

Figure 3

Balance functions plotted as a function of relative azimuthal angle are additionally constrained by the angle of the first charge, ${\varphi }_1$, which is measured relative to the reaction plane. The in-plane balance function, ${\varphi }_1\approx 0$, is significantly narrower than the the out-of-plane balance function, ${\varphi }_1\approx {90}^{\circ }$, due to the stronger collective flow. When ${\varphi }_1\approx {45}^{\circ }$ the balance function skew toward negative $\mathrm{\Delta }\varphi$ because the balancing charge is more likely to be found closer to the reaction plane, where more particles are emitted. The model calculations (blue lines) have been scaled by a factor of 0.94 to match the normalization of the preliminary experimental results from STAR [7] (red stars). After adjusting the normalization the experimental and model results are in remarkable agreement.

Figure 4

The contribution to the correlator ${\gamma }_p$ from local charge conservation superimposed onto elliptic flow from the model is compared to measurements from the STAR Collaboration [29]. The dashed green line shows contributions from correlations from the hydrodynamic stage, while the dotted line represents correlations born in the cascade. The sum (solid blue line) is $\approx 10–15\%$ higher than the data. Thus, the combination of charge conservation and flow more than accounts for the observed correlation, which has been proposed as a signal of the chiral magnetic effect.