An extended $R_{{\mathrm{\Psi }}_m}^{(2)}(\mathrm{\Delta }{S}_2)$ correlator for detecting and characterizing the Chiral Magnetic Wave

The extended $R_{{\mathrm{\Psi }}_m}^{(2)}(\mathrm{\Delta }{S}_2)$ correlator is presented and examined for its efficacy to detect and characterize the quadrupole charge separation ($\mathrm{\Delta }{S}_2$) 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 $R_{{\mathrm{\Psi }}_2}^{(2)}(\mathrm{\Delta }{S}_2)$ and $R_{{\mathrm{\Psi }}_3}^{(2)}(\mathrm{\Delta }{S}_2)$ correlators, relative to the second- (${\mathrm{\Psi }}_2$) and third-order (${\mathrm{\Psi }}_3$) event planes. The tests also indicate a level of sensitivity that would allow for robust experimental characterization of the CMW signal.