First Simultaneous Determination of Inclusive and Exclusive | V u b |
The first simultaneous determination of the absolute value of the Cabibbo-Kobayashi-Maskawa matrix element V ub using inclusive and exclusive decays is performed with the full Belle data set at the $Υ$(4S) resonance, corresponding to an integrated luminosity of 711 fb -1 . We analyze collision events in which one B meson is fully reconstructed in hadronic modes. This allows for the reconstruction of the hadronic X u system of the semileptonic b → $πℓe_ℓ$ decay. We separate exclusive B → $πℓ\overline{ν}_ℓ$ decays from other inclusive B → $X_uℓ\overline{ν}_ℓ$ and backgrounds with a two-dimensional fit that utilizes the number of charged pions in the X u system and the four-momentum transfer q 2 between the B and X u systems. Combining our measurement with information from lattice QCD and QCD calculations of the inclusive partial rate as well as external experimental information on the shape of the B → $πℓe_ℓ$ form factor, we determine |$V^{excl}_{ub}$| = (3.78 ± 0.23 ± 0.16 ± 0.14) × 10 -3 and |$V^{incl}_{ub}$| = (3.88 ± 0.20 ± 0.31 ± 0.09) x 10 -3 , respectively, with the uncertainties being the statistical error, systematic errors, and theory errors. The ratio of |$V^{excl}_{ub}$|/|$V^{incl}_{ub}$| 0.97 ± 0.12 is compatible with unity.