Operator product expansion sum rules for heavy flavor transitions and the determination of ‖Vcb‖

We derive a model-independent upper bound for the axial-vector form factor of the B→${\mathit{D}}^{\mathrm{*}}$ transition at zero recoil, ${\mathit{F}}_{\mathit{B}\to \mathit{D}}^{\mathrm{*}}$. The form factor turns out to be noticeably less than unity. The deviation ${\mathit{F}}_{\mathit{B}\to \mathit{D}}^{\mathrm{*}}$ from unity is larger than previously anticipated. Using our estimate we extract ‖${\mathit{V}}_{\mathit{c}\mathit{b}}$‖ from the measured exclusive rate of B→${\mathit{D}}^{\mathrm{*}}$lν extrapolated to the point of zero recoil. The central ‘‘exclusive’’ value of ‖${\mathit{V}}_{\mathit{c}\mathit{b}}$‖ is in agreement with the value obtained from the inclusive semileptonic width Γ(B→${\mathit{X}}_{\mathit{c}}$lν). We argue that the theoretical uncertainty in determining ‖${\mathit{V}}_{\mathit{c}\mathit{b}}$‖ from the total inclusive width is significantly reduced if a constraint on the quark mass difference ${\mathit{m}}_{\mathit{b}}$-${\mathit{m}}_{\mathit{c}}$ stemming from the heavy quark expansion is taken into account.