Reappraisal of SU(3)-flavor breaking in $B\rightarrow DP$

Abstract

In light of recently found deviations of the experimental data from predictions from QCD factorization for $B_{(s)}\rightarrow D_{(s)}P$ decays, where $P=\{\pi,K\}$, we systematically probe the current status of the SU(3)$_F$ expansion from a fit to experimental branching ratio data without any further theory input. We find that the current data are in agreement with the power counting of the SU(3)$_F$ expansion. While the SU(3)$_F$ limit is excluded at $>5\sigma$, amplitude-level SU(3)$_F$-breaking contributions of $\sim 20\%$ suffice for an excellent description of the data. SU(3)$_F$ breaking is needed in tree ($>5\sigma$) and color-suppressed tree ($2.4\sigma$) diagrams. We are not yet sensitive to SU(3)$_F$ breaking in exchange diagrams. From the underlying SU(3)$_F$ parametrization we predict the unmeasured branching ratios $\mathcal{B}(\overline{B}_s^0\rightarrow \pi^- D^+) = 2 \mathcal{B}(\overline{B}_s^0\rightarrow \pi^0 D^0) = [0.3, 7.2] \times 10^{-6}$ of suppressed decays that can be searched for at the LHCb experiment.