  A Multi-Phase Transport (AMPT) model is used to study the detection
sensitivity of two of the primary correlators -- $\Delta\gamma$ and
$R_{\Psi_{2}}$ -- employed to characterize charge separation induced by the
Chiral Magnetic Effect (CME). The study, performed relative to several event
planes for different input "CME signals", indicates a detection threshold for
the fraction $f_{\rm CME}=\Delta\gamma_{\rm CME}/\Delta\gamma$, which renders
the $\Delta\gamma$-correlator insensitive to values of the Fourier dipole
coefficient $a_1 \lesssim 2.5\%$, that is larger than the purported
signal(signal difference) for ion-ion(isobaric) collisions. By contrast, the
$R_{\Psi_{2}}$ correlator indicates concave-shaped distributions with inverse
widths ($\mathrm{\sigma^{-1}_{R_{\Psi_2}}}$) that are linearly proportional to
$a_1$, and independent of the character of the event plane used for their
extraction. The sensitivity of the $R_{\Psi_{2}}$ correlator to minimal
CME-driven charge separation in the presence of realistic backgrounds, could
aid better characterization of the CME in heavy-ion collisions.
