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

Krohn, J.-F.*; Tanida, Kiyoshi   ; Belle Collaboration*; 198 of others*

Using $$(771.6 pm 10.6) times 10^6$$ $$Bbar{B}$$ 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.

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