Using $(771.6 \pm 10.6) \times 10^6$ $B\bar{ B}$ meson pairs recorded by the Belle experiment at the KEKB $e^+ e^-$ collider, we report the branching fractions $\mathcal{ B}(\bar{ B}^0 \to D^{ *+} \pi^-) = (2.62 \pm 0.02 \pm 0.09)\times 10^{ -3}$ and $\mathcal{ B}(\bar{ B}^0 \to D^{ *+} K^-) = (2.22 \pm 0.06 \pm 0.08)\times 10^{ -4}$; the quoted uncertainties are statistical and systematic, respectively. A measurement of the ratio of these branching fractions is also presented, $\mathcal{ R}_{ K/\pi}=\mathcal{ B}(\bar{ B} \to D^{ *+}K^-) /\mathcal{ B}( \bar{ B} \to D^{ *+}\pi^-) = (8.41 \pm 0.24 \pm 0.13)\times 10^{ -2}$, where systematic uncertainties due to the $D^{ *+}$ meson reconstruction cancel out. Furthermore, we report a new QCD factorization test based on the measured ratios for $\bar{ B} \to D^{ *+}h^-$ and $\bar{ B} \to D^{ *+}\ell^-\nu$ decays at squared momentum transfer values equivalent to the mass of the $h = \pi$ or $K$ hadron. The parameters $|a_1(h)|$ are measured to be $|a_1(\pi)|= 0.884 \pm 0.004 \pm 0.003 \pm 0.016$ and $|a_1(K)|=0.913 \pm 0.019 \pm 0.008 \pm 0.013$, where the last uncertainties account for all external inputs. These values are approximately $15\%$ lower than those expected from theoretical predictions. Subsequently, flavor $SU(3)$ symmetry is tested by measuring the ratios for pions and kaons, $|a_1(K)|^2/ |a_1(\pi)|^2=1.066 \pm 0.042 \pm 0.018 \pm 0.023$, as well as for different particle species. The ratio is consistent with unity and therefore no evidence for $SU(3)$ symmetry breaking effects is found at the $5\%$ precision level.
Categories: hep-ex