Azimuthal angle dependence of the charge imbalance from charge conservation effects

The experimental search for the chiral magnetic effect in heavy-ion collisions is based on charge-dependent correlations between emitted particles. Recently, a sensitive observable comparing event-by-event distributions of the charge splitting projected on the directions along and perpendicular to the direction of the elliptic flow has been proposed. The results of a (3 + 1)-dimensional hydrodynamic model show that the preliminary experimental data of the STAR Collaboration can be explained as due to background effects, such as resonance decays and local charge conservation in the particle production. A related observable based on the third-order harmonic flow is proposed to further investigate such background effects in charge-dependent correlations.

Figure 1

The correlator $R\left(\mathrm{\Delta }S\right)$ [Eq. (4)] for Pb + Pb collisions at $\sqrt{s}=2760\mathrm{GeV}$ with $0–5\%$ (a), $30–40\%$ (b), and $70–80\%$ centrality (c). The dotted lines denote the results for primordial particles only, with no charge-dependent correlations. The dashed lines represent the results of the simulations including particles from resonance decays. The solid lines represent the results of the model with local charge conservation and resonance decays included. For clarity, in all figures statistical errors are shown only for one of the calculations.

Figure 2

Same as in Fig. 1 but for $p$ + Pb collisions at $\sqrt{s}=5020\mathrm{GeV}$ with centrality $0–3\%$.

Figure 3

Same as in Fig 1 but for Au + Au collisions at $\sqrt{s}=200\mathrm{GeV}$ and centrality $30–40\%$.

Figure 4

In- and out-of-plane charge imbalance distributions for Au + Au collisions at $\sqrt{s}=200\mathrm{GeV}$ and centrality $30–40\%$.

Figure 5

Same as in Fig. 1 but for the third-order event plane [Eq. (10)].

Figure 6

Same as in Fig. 5 but for $p$ + Pb collisions at $\sqrt{s}=5020\mathrm{GeV}$ with centrality $0–3\%$.

Figure 7

Same as in Fig. 5 but for Au + Au collisions at $\sqrt{s}=200\mathrm{GeV}$ and centrality $30–40\%$.

Figure 8

The correlator $R\left(\mathrm{\Delta }S\right)$ in Pb + Pb collisions at $\sqrt{s}=2070\mathrm{GeV}$ and centrality $30–40\%$. The solid line denotes the result with a perfect event-plane resolution, and the dashed and dotted lines for the event plane defined from charged particles with $2<\left|\eta \right|<4$. The results from the model including resonance decays is denoted with the dotted line and the calculation with resonances and local charge conservation with the dashed line.

Figure 9

Same as in Fig. 8 but for Au + Au collisions at $\sqrt{s}=200\mathrm{GeV}$ and centrality $30–40\%$.

Figure 10

Same as in Fig. 8 but for the correlator $R_3\left(\mathrm{\Delta }S\right)$ defined with respect to the third-order event plane.

Figure 11

Same as in Fig. 9 but for the correlator $R_3\left(\mathrm{\Delta }S\right)$ defined with respect to the third-order event plane.