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

Abstract

Decays of neutral B mesons originating from $b\to Dr$ $(r\in \{s,d\})$ processes, i.e. $B_d\to D{K}_{S(L)}$, $B_s\to D{\eta }^{{(}^{\prime })},D\varphi ,...$ $(r=s)$ and $B_s\to D{K}_{S(L)}$, $B_d\to D{\pi }^0,D{\rho }^0,...$ $(r=d)$ 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.

Comments: 37 pages, 5 figures, sign error in factorization prediction for cos(delta) corrected and numerical examples modified accordingly, conclusions unchanged