Improved methods for observing $\mathrm{CP}$ violation in $B^{\pm }\to \mathrm{KD}$ and measuring the CKM phase $\gamma$

Various methods are discussed for obtaining the CKM angle $\gamma$ through the interference of the charged B-meson decay channels $B^{-}\to K^{-}{D}^0$ and $B^{-}\to K^{-}{D}^0$ where the $D^0$ and $D^0$ decay to common final states. It is found that choosing final states which are not $\mathrm{CP}$ eigenstates can lead to large direct $\mathrm{CP}$ violation which can give significant bounds on $\gamma$ without any theoretical assumptions. If two or more modes are studied, $\gamma$ may be extracted with a precision on the order of $\pm 15°$ given $\sim {10}^8$ B-mesons. We also discuss the case of three body decays of the D where additional information may be obtained from the distribution of the D decay products and consider the impact of $D\overline{D}$ oscillations.