A Closer Look at $B_{d,s}\to D f_r$ Decays and Novel Avenues to Determine $\gamma$

Decays of neutral B mesons originating from $b\to D r$ $(r\in\{s,d\})$ processes, i.e. $B_d\to DK_{S(L)}$, $B_s\to D\eta^{(')}, D\phi, ...$ $(r=s)$ and $B_s\to DK_{S(L)}$, $B_d\to D\pi^0, D\rho^0, ...$ $(r=d)$ modes, offer valuable insights into CP violation. Here the neutral $D$ mesons may be observed through $D\to f_\pm$ or $D\to f_{NE}$, where $f_\pm$ and $f_{NE}$ are CP eigenstates and CP non-eigenstates, respectively. Recently, we pointed out that ``untagged'' and mixing-induced CP-violating $B_{d,s}\to D_\pm f_s$ observables provide a very efficient, theoretically clean determination of the angle $\gamma$ of the unitarity triangle. Here we perform a more detailed analysis of the $B_{d,s}\to D[\to f_\pm]f_s$ channels, and focus on $B_{d,s}\to D[\to f_{NE}] f_s$, where interference effects between Cabibbo-favoured and doubly Cabibbo-suppressed D-meson decays lead to complications. We show that $\gamma$ can nevertheless be determined in an elegant and essentially unambiguous manner from the $B_{d,s}\to D[\to f_{NE}]f_s$ observables with the help of the corresponding ``untagged'' $B_{d,s}\to D[\to f_\pm]f_s$ measurements. Moreover, we may also extract hadronic B- and D-decay parameters. Several interesting features of decays of the kind $B_{d,s}\to D f_d$ are also pointed out.