Bdecay shape variables and the precision determination of|Vcb|andmb

We present expressions for shape variables of B decay distributions in several different mass schemes, to order ${\alpha }_s^2{\beta }_0$ and ${\Lambda }_{\mathrm{QCD}}^3{/m}_b^3.$ Such observables are sensitive to the b quark mass and matrix elements in the heavy quark effective theory, and recent measurements allow precision determinations of some of these parameters. We perform a combined fit to recent experimental results from CLEO, BABAR, and DELPHI, and discuss the theoretical uncertainties due to nonperturbative and perturbative effects. We discuss the possible discrepancy between the OPE prediction, recent BABAR results and the measured branching fraction to D and $D^{*}$ states. We find $|V_{\mathrm{cb}}|=(40.8\mathrm{}\pm 0.9)\times {10}^{-3}$ and $m_b^{1S}=4.74\mathrm{}\pm 0.10\mathrm{GeV},$ where the errors are dominated by experimental uncertainties.