Investigating event-shape methods in the search for the chiral magnetic effect in relativistic heavy ion collisions

The chiral magnetic effect (CME) is a phenomenon in which electric charge is separated by a strong magnetic field from local domains of chirality imbalance and parity violation in quantum chromodynamics. The CME-sensitive observable, the charge-dependent three-point azimuthal correlator $\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}$, is contaminated by a major physics background proportional to the particle's elliptic flow anisotropy ${v}_{2}$. Event-shape engineering (ESE) binning events in dynamical fluctuations of ${v}_{2}$ and event-shape selection (ESS) binning events in statistical fluctuations of ${v}_{2}$ are two methods to search for the CME by projecting $\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}$ to the measured anisotropy ${v}_{2}=0$ intercept. We conduct a systematic study of these two methods using physics models as well as toy model simulations. It is observed that the ESE method fulfills the general premise of measuring the CME but is statistically hungry. It is found that the intercept from the ESS method depends on the details of the event content, such as the mixtures of background-contributing sources, because of statistical fluctuations of intertwining variables used in the method, and is thus not practically useful to measure the CME.