New insights of multi-particle azimuthal correlations with symmetric cumulants in p-p, p-Pb, and Pb-Pb collisions

The first comparison of anisotropy harmonics ($v_{n}$, n = 2-4) and event-by-event correlations of different orders between p--p (13 TeV), p--Pb (5.02 and 8.16 TeV) and Pb--Pb (5.02 TeV) as a function of multiplicity is presented. The $v_{n}$ coefficients are extracted via long-range ($\left | \Delta\eta \right | >$~2) two-particle correlations reaching a very-high-multiplicity region. Event-by-event correlations among $v_{2}$, $v_{3}$ and $v_{4}$ are measured using the four-particle symmetric cumulant (SC(n,m), n = 2, m = 3, 4). For high-multiplicity (more than 100 tracks) events, $v_{2}$ is found to have a negative correlation with the $v_{3}$, while the $v_{2}$ and $v_{4}$ are positively correlated. Normalized by the two-particle $v_{n}$, the SC(2,3) are quantitatively similar for p-Pb and Pb-Pb data, while a strong system size dependence is observed for SC(2,4). These new data provide important insights to the origin of collectivity observed in small collision systems.