Investigating the Event-Shape Methods in Search for the Chiral Magnetic Effect in Relativistic Heavy Ion Collisions

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 (QCD). The CME-sensitive observable, charge-dependent three-point azimuthal correlator Δγ, is contaminated by a major physics background proportional to the particle's elliptic anisotropy v₂. Event-shape engineering (ESE) binning events in dynamical fluctuations of v₂ and event-shape selection (ESS) binning events in statistical fluctuations of v₂ are two methods to search for the CME by projecting Δγ to the v₂=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 requires significantly more statistics than the ESS method to achieve the same statistical precision of the intercept. 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, and thus is not a clean measure of the CME.