Revealing long-range multi-particle collectivity in small collision systems via subevent cumulants

Abstract

Multi-particle azimuthal cumulants, often used to study collective flow in high-energy heavy-ion collisions, have recently been applied in small collision systems such as $pp$ and $p$+A to extract the second-order azimuthal harmonic flow $v_2$. Recent observation of four-, six- and eight-particle cumulants with "correct sign" $c_2\{4\}<0, c_2\{6\}>0, c_2\{8\}<0$ and approximate equality of the inferred single-particle harmonic flow, $v_2\{4\}\approx v_2\{6\}\approx v_2\{8\}$, have been used as strong evidence for a collective emission of all soft particles produced in the collisions. We show that these relations in principle could be violated due to the non-Gaussianity in the event-by-event fluctuation of flow and/or non-flow. Furthermore, we show, using $pp$ events generated with the PYTHIA model, that $c_2\{2k\}$ obtained with standard cumulant method are dominated by non-flow from dijets. An alternative cumulant method based on two or more $\eta$-separated subevents is proposed to suppress the dijet contribution. The new method is shown to be able to recover a flow signal as low as 4\% imposed on the PYTHIA events, independently of how the event activity class is defined. Therefore the subevent cumulant method offers a more robust way of studying collectivity based on the existence of long-range azimuthal correlations between multiple distinct $\eta$ ranges. The prospect of using the subevent cumulants to study collective flow in A+A collisions, in particular its longitudinal dynamics, is discussed.