A new sine observable, RΨ 2 (∆S), has been proposed to measure the chiral magnetic effect (CME) in heavy-ion collisions; ∆S = sin ϕ+ − sin ϕ− , where ϕ± are azimuthal angles of positively and negatively charged particles relative to the reaction plane and averages are event-wise, and RΨ 2 (∆S) is a normalized event probability distribution. Preliminary STAR data reveal concave RΨ 2 (∆S) distributions in 200 GeV Au+Au collisions. Studies with a multiphase transport (AMPT) and anomalous-viscous Fluid Dynamics (AVFD) models show concave RΨ 2 (∆S) distributions for CME signals and convex ones for typical resonance backgrounds. A recent hydrodynamic study, however, indicates concave shapes for backgrounds as well. To better understand these results, we report a systematic study of the elliptic flow (v2) and transverse momentum (pT ) dependences of resonance backgrounds with toy-model simulations and central limit theorem (CLT) calculations. It is found that the concavity or convexity of RΨ 2 (∆S) depends sensitively on the resonance v2 (which yields different numbers of decay π + π − pairs in the in-plane and out-of-plane directions) and pT (which affects the opening angle of the decay π + π − pair). Qualitatively, low pT resonances decay into large opening-angle pairs and result in more "back-to-back" pairs out-of-plane, mimicking a CME signal, or a concave RΨ 2 (∆S). Supplemental studies of RΨ 3 (∆S) in terms of the triangular flow (v3), where only backgrounds exist but any CME would average to zero, are also presented. PACS numbers: 25.75.-q, 25.75.-Gz, 25.75.-Ld Nn 1 sin(ϕ − ), (2)where φ is the particle azimuthal angle in the laboratory frame and ϕ is therefore the azimuthal angle relative to the second-order harmonic plane Ψ 2 (as a proxy for the unmeasured reaction plane). Subscripts (+, −) indicate arXiv:1803.02860v3 [nucl-th]