Nonflow Subtraction Beyond Two-Particle Correlations

Establishing collective flow in small collision systems is crucial 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 particle multiplicities $N$. 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 clean nonflow estimators, since the $p_{\rm T}$-integrated dipolar flow nearly vanishes. Using \HIJING{} as a controlled nonflow-only environment, we test the subtraction for three target observables ($\langle v_2^2\rangle$, $\langle v_2^2\delta p_{\rm T}\rangle$, and $c_2\{4\}$) in O+O and $d$+Au at $\sqrt{s_{\rm NN}} = 5.36$ TeV and 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.