Measurement of multi-particle azimuthal correlations with the subevent cumulant method in $pp$ and $p+$Pb collisions with the ATLAS detector

The measurement of four-particle cumulant elliptic flow coefficients $c_{2}\{4\}$ 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. The values of $c_{2}\{4\}$ are calculated using the standard cumulant method and recently proposed two subevent and three subevent methods. The two subevent method is found to be less sensitive to short-range correlations, and three subevent method further suppresses dijet correlations. The three subevent method gives a negative $c_{2}\{4\}$, and thus a well-defined $v_{2}\{4\}=(-c_{2}\{4\})^{1/4}$, in these collision systems. The magnitude of the $c_{2}\{4\}$ is found to be nearly independent of $\langle N_{\text{ch}}\rangle$. Furthermore, $v_{2}\{4\}$ is found to be smaller than $v_{2}\{2\}$ measured using the two-particle correlation method, as expected for a long-range 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.