A novel observable for $CP$ violation in multi-body decays and its application potential to charm and beauty meson decays

Abstract

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

Comments: 13 pages, accepted for publication in PLB, title changed