Measurement of multi-particle azimuthal correlations with the subevent cumulant method with the ATLAS detector

The measurement of four-particle cumulant and anisotropic elliptic flow coefficient for the second harmonic, $c_{2}\{4\}$ and $v_{2}\{4\}$, are presented using $pp$ data at $\sqrt{s}=5.02$ and $\sqrt{s}=13$ TeV, and $p+$Pb data at $\sqrt{s_{\text{NN}}}=5.02$ TeV. These measurements aim to assess collective nature of multi-particle production. While collectivity is well established in $p$+Pb and Pb+Pb collisions, because of larger non-flow contributions, its evidence in $pp$ collisions is contested. The values of $c_{2}\{4\}$ are calculated using the standard cumulant method and recently proposed two and three subevent methods, which can further suppress the non-flow contributions in small systems. In these collisions systems, the three subevent method gives a negative $c_{2}\{4\}$, and thus a well-defined $v_{2}\{4\}$. The magnitude of $c_{2}\{4\}$ is found to be nearly independent of $\langle N_{\text{ch}} \rangle$ and third harmonic $c_{3}\{4\}$ is consistent with 0. $v_{2}\{4\}$ is found to be smaller than $v_{2}\{2\}$ measured using the two-particle correlation method, as expected for a collective behavior. Following a recent model framework, the measured values of $v_{2}\{4\}$ and $v_{2}\{2\}$ are used to probe the number of sources in the initial state collision geometry.