Measurement of Branching Fraction and $CP$ Asymmetry in $B^-\rightarrow D^0_{DCS} \pi^-$

The CKM angle $\gamma$ can be cleanly determined from $CP$~asymmetries in suppressed $B^{-}\to D^0 K^-$ decays, where it enters at tree-level. The decays where the $D^{0}$ goes into the doubly Cabibbo-suppressed mode $D^0_{DCS} \rightarrow K^- \pi^+$ are particularly useful in this respect, but they are very rare and have not yet been observed, while only a few tens of events have been reconstructed for the less rare $B^- \rightarrow D^0_{DCS}\pi^-$ decay mode. We present the first analysis of these modes performed in $p\bar p$~collisions, using a sample of about 2~fb$^{-1}$ of data collected by the CDF Collaboration with an impact-parameter trigger. We report preliminary measurements of the branching fraction and $CP$~asymmetry for the $B^- \rightarrow D_{DCS}\ \pi^-$ decay mode.