Hadronic Mass Moments in Inclusive Semileptonic $\mathit{B}$ Meson Decays

We have measured the first and second moments of the hadronic mass-squared distribution in $B\to X_c\ell \nu$, for $P_{\mathrm{lepton}}>1.5\mathrm{}\mathrm{GeV}/c$. We find $〈M_X^2-{\overline{M}}_D^2〉=0.251\mathrm{}\pm 0.066{\mathrm{GeV}}^2$, $\mathbf{〈}(M_X^2-〈M_X^2〉{)}^2\mathbf{〉}=0.576\mathrm{}\pm 0.170{\mathrm{GeV}}^4$, where ${\overline{M}}_D$ is the spin-averaged $D$ meson mass. From that first moment and the first moment of the photon energy spectrum in $b\to s\gamma$, we find the heavy quark effective theory parameter ${\lambda }_1$ (in the modified minimal subtraction renormalization scheme, to order ${1/M}_B^3$ and ${\beta }_0{\alpha }_s^2$) to be $-0.24\mathrm{}\pm 0.11{\mathrm{GeV}}^2$. Using these first moments and the $B$ semileptonic width, and assuming parton-hadron duality, we obtain $|V_{\mathrm{cb}}|=0.0404\mathrm{}\pm 0.0013$.