Responses of the chiral-magnetic-effect-sensitive sine observable to resonance backgrounds in heavy-ion collisions

A new sine observable, $R_{Psi_2}(Delta S)$, has been proposed to measure the chiral magnetic effect (CME) in heavy-ion collisions; $Delta S = left langle sin varphi_+ right rangle - left langle sin varphi_- right rangle$, where $varphi_pm$ are azimuthal angles of positively and negatively charged particles relative to the reaction plane and averages are event-wise, and $R_{Psi_2}(Delta S)$ is a normalized event probability distribution. Preliminary STAR data reveal concave $R_{Psi_2}(Delta S)$ distributions in 200 GeV Au+Au collisions. Studies with a multiphase transport (AMPT) and anomalous-viscous Fluid Dynamics (AVFD) models show concave $R_{Psi_2}(Delta S)$ 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 ($v_{2}$) and transverse momentum ($p_{T}$) dependences of resonance backgrounds with toy-model simulations and central limit theorem (CLT) calculations. It is found that the concavity or convexity of $R_{Psi_2}(Delta S)$ depends sensitively on the resonance $v_2$ (which yields different numbers of decay $pi^+pi^-$ pairs in the in-plane and out-of-plane directions) and $p_T$ (which affects the opening angle of the decay $pi^+pi^-$ pair). Qualitatively, low $p_{T}$ 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 $R_{Psi_2}(Delta S)$. Supplemental studies of $R_{Psi_3}(Delta S)$ in terms of the triangular flow ($v_3$), where only backgrounds exist but any CME would average to zero, are also presented.