Event-plane correlations and hydrodynamic simulations of heavy ion collisions

We use a nonlinear response formalism to describe the Event-plane correlations measured by the ATLAS Collaboration. With one exception $\left(〈cos(2{\Psi }_2-6{\Psi }_3+4{\Psi }_4)〉\right)$, the Event-plane correlations are qualitatively reproduced by considering the linear and quadratic response to the lowest cumulants. For the lowest harmonics such as $〈cos(2{\Psi }_2+3{\Psi }_3-5{\Psi }_5)〉$, the correlations are quantitatively reproduced, even when the naive Glauber model prediction has the wrong sign relative to experiment. The quantitative agreement for the higher plane correlations (especially those involving ${\Psi }_6$) is not as good. The centrality dependence of the correlations is naturally explained as an average of the linear and quadratic response.

Figure 1

Participant two-plane correlations from the phobos Monte Carlo Glauber model [17] as measured by the cumulant and moment expansions. The measured event-plane correlations [10] are presented for reference and as a point of contact and are not supposed to be directly compared to the Glauber model results.

Figure 2

Participant three-plane correlations from the phobos Monte Carlo Glauber model [17] as measured by the cumulant and moment expansions. The measured event-plane correlations [10] are presented for reference and as a point of contact and are not supposed to be directly compared to the Glauber model results.

Figure 3

Two-plane correlations using the nonlinear response formalism. Here $\eta /s=1/4\pi$ for phobos Monte Carlo Glauber initial conditions. The data are from the ATLAS Collaboration [10]. The solid lines indicate the high-resolution limit, Eq. (2.17), while the dashed lines indicate the low-resolution limit, Eq. (2.18).

Figure 4

Three-plane correlations using the nonlinear response formalism. Here $\eta /s=1/4\pi$ for phobos Monte Carlo Glauber initial conditions. The data are from the ATLAS Collaboration [10]. The solid lines indicate the high-resolution limit, Eq. (2.17), while the dashed lines indicate the low-resolution limit, Eq. (2.18).

Figure 5

A comparison of the two-plane correlations in the high-resolution limit for two different Glauber models, glissando [16] and the phobos Glauber [17]. The solid lines (uncut) include the negative response in peripheral collisions due to a large $\delta f$, while the dashed lines (cut) truncate the negative response; see Sec. 3.

Figure 6

A comparison of the three-plane correlations in the high-resolution limit for two different Glauber models, glissando [16] and the phobos Glauber [17]. The solid lines (uncut) include the negative response in peripheral collisions due to a large $\delta f$, while the dashed lines (cut) truncate the negative response; see Sec. 3.

Figure 7

The separate contributions of the linear and nonlinear response to a two-plane correlation, $〈cos(4{\Psi }_4-4{\Psi }_2)〉$, and a three-plane correlation, $〈cos(2{\Psi }_2+3{\Psi }_3-5{\Psi }_5)〉$. The dashed lines show the naive Glauber expectation (see text). The data are from Ref. [10].