Strategies for measuring $\gamma$ from the decay channels $B^{0}_{d} \to D^{\mp} \pi^{\pm}$ and $B^{0}_{s} \to D^{\mp}_{s} K^{\pm}$ at LHCb

Two possible measurements of the CKM angle $gamma$ at LHCb are evaluated:from the decay mode $B^0_d \rightarrow D^- pi^+$, and from the combined analysis of the decay modes $B^0_d \rightarrow D^- pi^+$ and $B^0_s \rightarrow D^-_s K^+$ under the conditions of U-spin symmetry. It is shown that the analysis of time dependent decay rate asymmetries in $B^0_d \rightarrow D^- pi^+$ can result in a precision of $sim 10^circ$ on $gamma$ after five years of data taking under certain theoretical assumptions. The combined extraction of $gamma$ from the decay modes $B^0_d \rightarrow D^- pi^+$ and $B^0_s \rightarrow D^-_s K^+$ is seen to allow an unambiguous extraction of $gamma$, with a precision of $sim 5^circ$ after five years of data taking.