Measurement of multi-particle azimuthal correlations 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 0.17 pb$^{-1}$ of $pp$ data at $\sqrt{s}=5.02$ TeV, 0.9 pb$^{-1}$ of $pp$ data at $\sqrt{s}=13$ TeV and 28 nb$^{-1}$ of $p$+Pb data at $\sqrt{s_{\rm{NN}}}=5.02$ TeV. The values of $c_{2}${4} are calculated as a function of average number of charged particles, $\left\langle N_{\rm{ch}} \right\rangle$, using the standard cumulant method and recently proposed two-subevent and three-subevent methods. The three-subevent method is found to be less sensitive to short-range correlations, originating mostly from jets. 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 $\left\langle N_{\rm{ch}} \right\rangle$. Furthermore, $v_2${4} is found to be smaller than the $v_2${2} measured using the two-particle correlation method, as expected for a long-range collective behaviour. 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.