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The search for the chiral magnetic effect (CME) in relativistic heavy-ioncollisions helps us understand the $\mathcal{CP}$ symmetry breaking in stronginteractions and the topological nature of the QCD vacuum. Since the backgroundand signal of the CME have different correlations with respect to the spectatorand participant planes, a two-plane method has been proposed to extract thefraction of the CME signal inside the CME observable of $\Delta\gamma$ from theexperimental measurements relative to the two planes. Using a multiphasetransport model with different strengths of the CME, we reexamine the two-planemethod in isobar collisions at $\sqrt{s_{_{\rm NN}}} = 200$ GeV. The ratios ofthe CME signal and background relative to the two different planes are found tobe different, which is inconsistent with the assumptions made in the currentexperimental measurements. The difference arises from the decorrelation of thechiral magnetic effect relative to spectator and participant planes, whichoriginates from final state interactions. Our finding suggests that the currentexperimental measurements may overestimate the fraction of the CME signal inthe CME observable in relativistic heavy-ion collisions.

On the difference between signal and background of the chiral magnetic  effect relative to spectator and participant planes in isobar collisions at  $\sqrt{s_{_{\rm NN}}} = 200$ GeV