Probing CP violation with time integrated decay rates into non-CP eigenstates

Many of the experiments proposed to look for interference CP violation in neutral B mesons concentrate on tagged decay into CP eigenstates. Aleksan, Dunietz, Kayser and Le Diberder have shown that one can also look for interference CP violation using tagged decays into non-CP eigenstates. In all these methods, one must trace the time dependence of the decays. In this article we discuss a new method to search for interference CP violation by using only time integrated rates into non-CP eigenstates. The method hinges on the comparison between the decays of $\Upsilon(4S)$ into $f f$, $\bar{f} \bar{f}$, and $f \bar{f}$, and also uses the rates for $l^+ f$ and $l^- f$. This method does not depend on how the $\Upsilon(4S)$ is produced; provided enough statistics, one can use both symmetric and asymmetric colliders.