A global analysis of ${\bar B}\to DP$ and ${\bar B} \to {\bar D} P$ decays

Abstract

Recently, a fit to the 15 measured branching ratios of ${\bar B} \to D P$ decays ($B = \{B^+, B^0, B_s^0\}$, $D = \{D^0, D^+, D_s^+\}$, $P \in \{π, K\}$) was performed under the assumption of flavor SU(3) symmetry [SU(3)$_F$]. A terrible fit was found: there was a $> 5σ$ disagreement with the SU(3)$_F$ limit of the Standard Model [SM$_{\rm{SU(3)}_F}$]. It was also found that this discrepancy can be removed by adding $\sim 20\%$ SU(3)$_F$-breaking effects. Now, the ${\bar B} \to D^0 P$ amplitudes can contribute to other observables (direct and indirect CP asymmetries) if they interfere with the amplitudes for ${\bar B} \to {\bar D}^0 P$ decays. This happens if the $D^0$ and ${\bar D}^0$ decay to the same final state (e.g., $K^+ K^-$, $π^+ π^-$, $K^\pm π^\mp$, etc.). In this paper, we perform a combined fit of ${\bar B} \to D P$ and ${\bar B} \to {\bar D} P$ decays, including all observables. We again find a $> 5σ$ disagreement with the SM$_{\rm{SU(3)}_F}$, and we find that the data can be explained if $\sim 60\%$ SU(3)$_F$-breaking effects are included.