Measurements of the branching fractions $\mathcal{B}({\overline{B}}^0\to D^{*+}{\pi }^{-})$ and $\mathcal{B}({\overline{B}}^0\to D^{*+}{K}^{-})$ and tests of QCD factorization

Using $(771.6\pm 10.6)\times {10}^{6}B\overline{B}$ meson pairs recorded by the Belle experiment at the KEKB $e^{+}{e}^{-}$ collider, we report the branching fractions $\mathcal{B}({\overline{B}}^0\to D^{*+}{\pi }^{-})=(2.62\pm 0.02\pm 0.09)\times {10}^{-3}$ and $\mathcal{B}({\overline{B}}^0\to D^{*+}{K}^{-})=(2.22\pm 0.06\pm 0.08)\times {10}^{-4}$; the quoted uncertainties are statistical and systematic, respectively. A measurement of the ratio of these branching fractions is also presented, ${\mathcal{R}}_{K/\pi }=\mathcal{B}(\overline{B}\to D^{*+}{K}^{-})/\mathcal{B}(\overline{B}\to D^{*+}{\pi }^{-})=(8.41\pm 0.24\pm 0.13)\times {10}^{-2}$, 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 $\overline{B}\to D^{*+}{h}^{-}$ and $\overline{B}\to D^{*+}{\ell }^{-}\nu$ 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.

Figure 1

Results of the fits to the $\mathrm{\Delta }E$ distributions in the $D^0\to K^{-}{\pi }^{+}$ channel of (a) ${\overline{B}}^0\to D^{*+}{K}^{-}$ and (b) ${\overline{B}}^0\to D^{*+}{\pi }^{-}$.

Figure 2

Results of the fits to the $\mathrm{\Delta }E$ distributions in the $D^0\to K^{-}2{\pi }^{+}{\pi }^{-}$ channel of (a) ${\overline{B}}^0\to D^{*+}{K}^{-}$ and (b) ${\overline{B}}^0\to D^{*+}{\pi }^{-}$.

Figure 3

Comparison of the branching fraction ratio measurements using the full data sample and the data subsamples with respect to previous measurements by (a) Belle [15] and BABAR [14], and (b) BABAR [12, 13] and CLEO-II [7]. The theoretical predictions are taken from Refs. [1, 32]. The inner uncertainty is statistical and the outer is the quadrature sum of both statistical and systematic uncertainties.

Figure 4

Comparison of the branching fraction ratio measurements using the full data sample and the data subsamples with respect to previous measurements by BABAR [14], LHCb [16] and the theoretical prediction from Ref. [32]. The inner uncertainty is statistical and the outer is the quadrature sum of both statistical and systematic uncertainties.

Figure 5

Semileptonic decay rates $d\mathrm{\Gamma }({\overline{B}}^0\to D^{*+}{\ell }^{-}\overline{\nu })/d{q}^2$ as a function of dilepton invariant mass squared determined from fits to Belle data and lattice QCD inputs from Fermilab-MILC and JLQCD, based on the method described in Ref. [20].

Figure 6

The extracted values of $|a_1(h)|$ from ${\overline{B}}^0\to D^{*+}{h}^{-}$, $h=\pi ,K,\rho ,K^{*},a_1$ using the three semileptonic input scenarios described in the text. The theory predictions are taken from Refs. [17, 32].