An extended $R^{(2)}_{\Psi_m}(\Delta S_2)$ correlator for detecting and characterizing the Chiral Magnetic Wave

The extended $R^{(2)}_{\Psi_{m}}(\Delta S_{2})$ correlator is presented and examined for its efficacy to detect and characterize the quadrupole charge separation ($\Delta S_{2}$) associated with the purported Chiral Magnetic Wave (CMW) produced in heavy-ion collisions. Sensitivity tests involving varying degrees of proxy CMW signals injected into events simulated with the Multi-Phase Transport Model (AMPT), show that the $R^{(2)}_{\Psi_{m}}(\Delta S_{2})$ correlator provides discernible responses for the background- and CMW-driven charge separation. This distinction could aid identification of the CMW via measurements of the $R^{(2)}_{\Psi_{2}}(\Delta S_{2})$ and $R^{(2)}_{\Psi_{3}}(\Delta S_{2})$ correlators, relative to the second- ($\Psi_2$) and third-order ($\Psi_3$) event planes. The tests also indicate a level of sensitivity that would allow for robust experimental characterization of the CMW signal.