Nonflow subtraction beyond two-particle correlations

Establishing collective flow in small collision systems is a crucial and necessary condition for pinning down the minimum conditions for quark-gluon plasma (QGP) formation. In two-particle correlations, nonflow has been subtracted with good control, pushing the reach of flow measurements down to very small event particle multiplicity $N$. However, the multi-particle nature of collectivity has not been established in the same $N$ regime, because the residual nonflow surviving the subevent procedure in multi-particle cumulants has never been quantified. We develop a general nonflow subtraction framework for $m$-particle cumulants, built around the approximate $1/N^{m-1}$ scaling of nonflow in the independent-source picture. Correlators containing $v_1$ serve as nonflow-dominated estimators, since the $p_{\\mathrm T}$-integrated dipolar flow is expected to be small. Using \\HIJING{} as a controlled nonflow-only environment, we test the subtraction for three target observables ($\\langle v_2^2\\rangle$, $\\langle v_2^2\\delta p_{\\mathrm T}\\rangle$, and $c_2\\{4\\}$) in O+O at $\\sqrt{s_{\\mathrm{NN}}} = 5.36$~TeV and 200~GeV and in $d$+Au at $\\sqrt{s_{\\mathrm{NN}}} = 200$~GeV. Most of the nonflow is removed, with residual fractions typically within 20--30\\% when converted to the two-particle level, though the best estimator differs across the three targets. We identify a multiplicity-reweighting correction, previously overlooked in two-particle correlations, that explains the long-standing undersubtraction of the naive $1/N$-scaling method; its impact grows as a power of the correlator order. The framework gives a systematic route to nonflow subtraction beyond two-particle correlations, broadening the class of multi-particle observables accessible to the small-system flow program.