Background: The chiral magnetic effect (CME) is extensively studied in heavy-ion collisions at RHIC and the LHC. An azimuthal correlator called $R_{Psi_{m}}$ was proposed to measure the CME. By observing the same $R_{Psi_{2}}$ and $R_{Psi_{3}}$ (convex) distributions from A Multi-Phase Transport (AMPT) model, by contrasting data and model as well as large and small systems and by event shape engineering (ESE), a recent preprint (arXiv:2006.04251v1) from STAR suggests that the $R_{Psi_{m}}$ observable is sensitive to the CME signal and relatively insensitive to backgrounds, and their Au+Au data are inconsistent with known background contributions. Purpose: We examine those claims by studying the robustness of the $R_{Psi_{m}}$ observable using AMPT as well as toy model simulations. We compare $R_{Psi_{m}}$ to the more widely used $Deltagamma$ azimuthal correlator to identify their commonalities and differences. Methods: We use AMPT to simulate Au+Au, p+Au, and d+Au collisions at $sqrt{s_{NN}} = 200 text{ GeV}$, and study the responses of $R_{Psi_{m}}$ to anisotropic flow backgrounds in the model. We also use a toy model to simulate resonance flow background and input CME signal to investigate their effects in $R_{Psi_{2}}$. Additionally we use the toy model to perform an ESE analysis to compare to STAR data as well as predict the degree of sensitivity of $R_{Psi_{2}}$ to isobar collisions with the event statistics taken at RHIC. ...
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