Gettingβ−αwithout penguin contributions

Oscillation effects in $B^0\to K_S{D}^0$ and related processes are considered to determine $\delta \equiv \beta -\alpha +\pi =2\mathrm{}\beta +\gamma .$ We suggest that $D^0$ decays to $\mathrm{CP}$ eigenstates used in concert with inclusive $D^0$ decays provide a powerful method for determining $\delta$ cleanly. The $\mathrm{CP}$ asymmetry is expected to be $\lesssim 40\%$ for $D^0$ decays to non-$\mathrm{CP}$ eigenstates and $\lesssim 80\%$ for decays to $\mathrm{CP}$ eigenstates. This method can lead to a fairly accurate determination of $\delta$ with ${O(10\mathrm{}}^8-{10}^9)$ B mesons.