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A detailed study of multi-particle azimuthal correlations is presented using$pp$ data at $\sqrt{s}=5.02$ and 13 TeV, and $p$+Pb data at$\sqrt{s_{\rm{NN}}}=5.02$ TeV, recorded with the ATLAS detector at the LHC. Theazimuthal correlations are probed using four-particle cumulants $c_{n}\{4\}$and flow coefficients $v_n\{4\}=(-c_{n}\{4\})^{1/4}$ for $n=2$ and 3, with thegoal of extracting long-range multi-particle azimuthal correlation signals andsuppressing the short-range correlations. The values of $c_{n}\{4\}$ areobtained as a function of the average number of charged particles per event,$\left\langle N_{\rm{ch}} \right\rangle$, using the recently proposedtwo-subevent and three-subevent cumulant methods, and compared with resultsobtained with the standard cumulant method. The three-subevent method is foundto be least sensitive to short-range correlations, which originate mostly fromjets with a positive contribution to $c_{n}\{4\}$. The three-subevent methodgives a negative $c_{2}\{4\}$, and therefore a well-defined $v_2\{4\}$, nearlyindependent of $\left\langle N_{\rm{ch}} \right\rangle$, which provides directevidence that the long-range multi-particle azimuthal correlations persist toevents with low multiplicity. Furthermore, $v_2\{4\}$ is found to be smallerthan the $v_2\{2\}$ measured using the two-particle correlation method, asexpected for long-range collective behavior. Finally, the measured values of$v_2\{4\}$ and $v_2\{2\}$ are used to estimate the number of sources relevantfor the initial eccentricity in the collision geometry.

physical review. c

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