Non-flow effects in correlation between harmonic flow and transverse momentum in nuclear collisions

A large anti-correlation signal between elliptic flow $v_2$ and average transverse momentum $[p_{\mathrm{T}}]$ was recently measured in small collision systems, consistent with a final-state hydrodynamic response to the initial geometry. This negative $v_2$-$[p_{\mathrm{T}}]$ correlation was predicted to change to positive correlation for events with very small charged particle multiplicity $N_{\mathrm{ch}}$ due to initial-state momentum anisotropies of the gluon saturation effects. However, the role of non-flow correlations is expected to be important in these systems, which is not yet studied. We estimate the non-flow effects in $pp$, $p$Pb and peripheral PbPb collisions using {\tt Pythia} and {\tt Hijing} models, and compare them with the experimental data. We show that the non-flow effects are largely suppressed using the rapidity-separated subevent cumulant method (details of the cumulant framework are also provided). The magnitude of the residual non-flow is much less than the experimental observation in the higher $N_{\mathrm{ch}}$ region, supporting the final-state response interpretation. In the very low $N_{\mathrm{ch}}$ region, however, the sign and magnitude of the residual non-flow depend on the model details. Therefore, it is unclear at this moment whether the sign change of $v_2$-$[p_{\mathrm{T}}]$ can serve as evidence for initial state momentum anisotropies predicted by the gluon saturation.