Measurements of the branching fractions $\mathcal{B}(\bar{B}{}^0\to D^{\ast +}\ddot{I}{€}^{-})$ and $\mathcal{B}(\bar{B}{}^0\to D^{\ast +}{K}^{-})$ and tests of QCD factorization

Abstract

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 $\mathcal{B}({\bar{B}}^0\to D^{\ast +}\ddot{I}{€}^{-})=(2.62\pm 0.02\pm 0.09)\times 10^{-3}$ and $\mathcal{B}({\bar{B}}^0\to D^{\ast +}{K}^{-})=(2.22\pm 0.06\pm 0.08)\times 10^{-4}$; the quoted uncertainties are statistical and systematic, respectively. A measurement of the ratio of these branching fractions is also presented, ${\mathcal{R}}_{K/\ddot{I}€}=\mathcal{B}(\bar{B}\to D^{\ast +}{K}^{-})/\mathcal{B}(\bar{B}\to D^{\ast +}\ddot{I}{€}^{-})=(8.41\pm 0.24\pm 0.13)\times 10^{-2}$, where systematic uncertainties due to the $D^{\ast +}$ meson reconstruction cancel out. Furthermore, we report a new QCD factorization test based on the measured ratios for $\bar{B}\to D^{\ast +}{h}^{-}$ and $\bar{B}\to D^{\ast +}{\ell }^{-}\hat{I}½$ decays at squared momentum transfer values equivalent to the mass of the $h=\ddot{I}€$ or $K$ hadron. The parameters $|a_1(h)|$ are measured to be $|a_1(\ddot{I}€)|=0.884\pm 0.004\pm 0.003\pm 0.016$ 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, $|a_1(K){|}^2/|a_1(\ddot{I}€){|}^2=1.066\pm 0.042\pm 0.018\pm 0.023$, 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.

13 pages, 6 figures