Correlations of flow harmonics in 2.76A TeV Pb--Pb collisions

Abstract

Using the event-by-event viscous hydrodynamics VISH2+1 with MC-Glauber, MC-KLN, and AMPT initial conditions, we investigate the correlations of flow harmonics, including the symmetric cumulants $S{C}^v(m,n)$, the normalized symmetric cumulants $NSC(m,n)$, and the Pearson correlation coefficients $C(v_m^2,v_n^2)$ in 2.76A TeV Pb--Pb collisions. We find $S{C}^v(m,n)$ is sensitive to both initial conditions and the specific shear viscosity $\hat{I}\cdot /s$. A comparison with the recent ALICE data show that our hydrodynamic calculations can qualitatively describe the data of $S{C}^v(3,2)$ and $S{C}^v(4,2)$ for various initial conditions, which demonstrate that $v_2$, $v_4$ are correlated and $v_2$, $v_3$ are anti-correlated. Meanwhile, the predicted symmetric cumulants $S{C}^v(5,2)$, $S{C}^v(5,3)$, and $S{C}^v(4,3)$ reveal that $v_2$ and $v_5$, $v_3$ and $v_5$ are correlated, $v_3$ and $v_4$ are anti-correlated in most centrality classes. We also find $NS{C}^v(3,2)$ and $C(v_3^2,v_2^2)$, which are insensitive to $\hat{I}\cdot /s$, are mainly determined by corresponding $NS{C}^{\epsilon }(3,2)$ and $C({\epsilon }_3^2,{\epsilon }_2^2)$ correlators from the initial state. In contrast, other $NS{C}^v(m,n)$ and $C(v_m^2,v_n^2)$ correlators are influenced by both initial conditions and $\hat{I}\cdot /s$, which illustrates the non-linear mode couplings in higher flow harmonics with $n\ge 4$.

10 pages, 7 figures