On a clean determination of $ϕ_2$

Abstract

We point out that time dependent study of four decay modes $B^0(t)\to \Dbar K_S$, $B^0(t)\to D K_S$ $\Bbar^0(t)\to \Dbar K_S$, and $\Bbar^0(t)\to D K_S$ allows us to measure $\sin(ϕ_1-ϕ_2)$ - contrary to previously obtained result that it measures $\sin(2ϕ_1+ϕ_3)$. The time dependent study of $B_s^0(t)\to D^\pm_sK^\mp$, and the study of $B^-\to K^-(D,\Dbar)\to K^-f$ decay where $D\to f$ is a doubly Cabibbo suppressed decay yield information on $ϕ_3$, as previusly expected.