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A novel observable measuring the $C\!P$ asymmetry in multi-body decays ofheavy mesons, which is called the forward-backward asymmetry induced $C\!P$asymmetry (FBI-$C\!P$A), $A_{CP}^{FB}$, is introduced. This observable has thedual advantages that 1) it can isolate the $C\!P$ asymmetry associated with theinterference of the $S$- and $P$-wave amplitude from that associated with the$S$- or $P$-wave amplitude alone; 2) it can effectively almost double thestatistics comparing to the conventionally defined regional $C\!P$ asymmetry.We also suggest to perform the measurements of FBI-$C\!P$A in some three-bodydecay channels of charm and beauty mesons.

A novel observable for $C\!P$ violation in multi-body decays and its application potential to charm and beauty meson decays