Examination of flow and nonflow factorization methods in small collision systems

Two particle correlations have been used extensively to study hydrodynamic flow patterns in heavy-ion collisions. In small collision systems, such as $p$$+$$p$ and $p$$+$$A$, where particle multiplicities are much smaller than in $A$$+$$A$ collisions, non-flow effects from jet correlations, momentum conservation, particle decays, etc. can be significant, even when imposing a large pseudorapidity gap between the particles. A number of techniques to subtract the non-flow contribution in two particle correlations have been developed by experiments at the Large Hadron Collider (LHC) and then used to measure particle flow in $p$$+$$p$ and $p$$+$Pb collisions. Recently, experiments at the Relativistic Heavy Ion Collider (RHIC) have explored the possibility of adopting these techniques for small collision systems at lower energies. In this paper, we test these techniques using Monte Carlo generators PYTHIA and HIJING, which do not include any collective flow, and AMPT, which does. We find that it is crucial to examine the results of such tests both for correlations integrated over particle transverse momentum $p_T$ and differentially as a function of $p_T$. Our results indicate reasonable non-flow subtraction for $p$$+$$p$ collisions at the highest LHC energies, while failing if applied to $p$$+$$p$ collisions at RHIC. In the case of $p$$+$Au collisions at RHIC, both HIJING and AMPT results indicate a substantial over-subtraction of non-flow for $p_{T}\gtrsim1~{\rm GeV}/c$ and hence an underestimate of elliptic flow.