Measurements of the branching fractions B(B¯0→D*+π−) and B(B¯0→D*+K−) and tests of QCD factorization

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Abstract

Using $(771.6\ifmmode\pm\else\textpm\fi{}10.6)\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }B\overline{B}$ meson pairs recorded by the Belle experiment at the KEKB ${e}^{+}{e}^{\ensuremath{-}}$ collider, we report the branching fractions $\mathcal{B}({\overline{B}}^{0}\ensuremath{\rightarrow}{D}^{*+}{\ensuremath{\pi}}^{\ensuremath{-}})=(2.62\ifmmode\pm\else\textpm\fi{}0.02\ifmmode\pm\else\textpm\fi{}0.09)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $\mathcal{B}({\overline{B}}^{0}\ensuremath{\rightarrow}{D}^{*+}{K}^{\ensuremath{-}})=\phantom{\rule{0ex}{0ex}}(2.22\ifmmode\pm\else\textpm\fi{}0.06\ifmmode\pm\else\textpm\fi{}0.08)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$; the quoted uncertainties are statistical and systematic, respectively. A measurement of the ratio of these branching fractions is also presented, ${\mathcal{R}}_{K/\ensuremath{\pi}}=\mathcal{B}(\overline{B}\ensuremath{\rightarrow}{D}^{*+}{K}^{\ensuremath{-}})/\phantom{\rule{0ex}{0ex}}\mathcal{B}(\overline{B}\ensuremath{\rightarrow}{D}^{*+}{\ensuremath{\pi}}^{\ensuremath{-}})=(8.41\ifmmode\pm\else\textpm\fi{}0.24\ifmmode\pm\else\textpm\fi{}0.13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$, 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 $\overline{B}\ensuremath{\rightarrow}{D}^{*+}{h}^{\ensuremath{-}}$ and $\overline{B}\ensuremath{\rightarrow}{D}^{*+}{\ensuremath{\ell}}^{\ensuremath{-}}\ensuremath{\nu}$ decays at squared momentum transfer values equivalent to the mass of the $h=\ensuremath{\pi}$ or $K$ hadron. The parameters $|{a}_{1}(h)|$ are measured to be $|{a}_{1}(\ensuremath{\pi})|=0.884\ifmmode\pm\else\textpm\fi{}0.004\ifmmode\pm\else\textpm\fi{}0.003\ifmmode\pm\else\textpm\fi{}0.016$ and $|{a}_{1}(K)|=0.913\ifmmode\pm\else\textpm\fi{}0.019\ifmmode\pm\else\textpm\fi{}0.008\ifmmode\pm\else\textpm\fi{}0.013$, 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, $|{a}_{1}(K){|}^{2}/|{a}_{1}(\ensuremath{\pi}){|}^{2}=\phantom{\rule{0ex}{0ex}}1.066\ifmmode\pm\else\textpm\fi{}0.042\ifmmode\pm\else\textpm\fi{}0.018\ifmmode\pm\else\textpm\fi{}0.023$, 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.

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