Measurement of four-particle cumulants and symmetric cumulants with subevent methods in small collision systems with the ATLAS detector

Measurements of symmetric cumulants SC(n,m)=⟨v2nv2m⟩−⟨v2n⟩⟨v2m⟩ for (n,m)=(2,3) and (2,4) and asymmetric cumulant AC(n) are presented in pp, p+Pb and peripheral Pb+Pb collisions at various collision energies, aiming to probe the long-range collective nature of multi-particle production in small systems. Results are obtained using the standard cumulant method, as well as the two-subevent and three-subevent cumulant methods. Results from the standard method are found to be strongly biased by non-flow correlations as indicated by strong sensitivity to the chosen event class definition. A systematic reduction of non-flow effects is observed when using the two-subevent method and the results become independent of event class definition when the three-subevent method is used. The measured SC(n,m) shows an anti-correlation between v2 and v3, and a positive correlation between v2 and v4. The magnitude of SC(n,m) is constant with Nch in pp collisions, but increases with Nch in p+Pb and Pb+Pb collisions. The normalized symmetric cumulants SC(n,m)/⟨v2n⟩⟨v2m⟩ are found to be independent of pT, suggesting vn-vm correlations reflect the global properties of the event. These measurements provide further evidence for long-range multi-particle collectivity, and quantify the nature of its event-by-event fluctuations.