A Toy Model for Estimation of the Event Plane Non-Flat Effect on an Elliptic Flow in Heavy Ion Collision

In heavy ion collision, the event plane is a key parameter defined as the plane composted by the impact parameter b and beam axis z. It is a crucial reference for various observables, which focus on the initial spatial anisotropy of the overlap region in heavy ion collision. We notice that in some recent heavy ion collision experiments, due to potentially inefficient or even the invalidity of experimental facilities, the reconstructed event plane, which is used in elliptic flow study, may be biased towards a non-flat distribution. In this study, we develop a toy model for fast estimation of the bias effect and its influence on the elliptic flow. The possible azimuthal bias of the detector is firstly studied by varying the part of its azimuthal information. We also study on the limit acceptance of the detector, which will be used to measure the particle of interest in an elliptic flow. The outcomes are presented by comparing the flow study results with or without the non-flat effect on the event plane.