Using the previous Belle measurement of the inclusive photon energy in $B\to X_s\gamma$ decays, we determine the first and second moments of this spectrum for minimum photon energies in the $B$ meson rest frame ranging from 1.8 to 2.3 GeV. Combining these measurements with recent Belle data on the lepton energy and hadronic mass moments in $B\to X_c\ell \nu$ decays, we perform fits to theoretical expressions derived in the 1S and kinetic mass schemes and extract the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $V_{cb}$, the $b$-quark mass, and other nonperturbative parameters. In the 1S scheme analysis we find $|V_{cb}|=(41.56\pm 0.68(\mathrm{\text{fit}})\pm 0.08({\tau }_B))\times {10}^{-3}$ and $m_b^{1\mathrm{S}}=(4.723\pm 0.055)\mathrm{GeV}$. In the kinetic scheme, we obtain $|V_{cb}|=(41.58\pm 0.69(\mathrm{\text{fit}})\pm 0.08({\tau }_B)\pm 0.58(\mathrm{th}))\times {10}^{-3}$ and $m_b^{\mathrm{kin}}=(4.543\pm 0.075)\mathrm{GeV}$.

• Received 10 March 2008

DOI:https://doi.org/10.1103/PhysRevD.78.032016