Determination of the $\overline{B}\to D^{*}\mathcal{l}\overline{\nu }$ decay width and $|V_{\mathrm{cb}}|$

In the standard model, the charged current of the weak interaction is governed by a unitary quark mixing matrix that also leads to CP violation. Measurement of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements is essential to searches for new physics, either through the structure of the CKM matrix, or a departure from unitarity. We determine the CKM matrix element $|V_{\mathrm{cb}}|$ using a sample of $3\times {10}^6$ $B\overline{B}$ events in the CLEO detector at the Cornell Electron Storage Ring. We determine the yield of reconstructed $B^0\to D^{*+}\mathcal{l}\overline{\nu }$ and $B^{-}\to D^{*0}\mathcal{l}\overline{\nu }$ decays as a function of w, the boost of the $D^{*}$ in the B rest frame, and from this we obtain the differential decay rate $d\Gamma /dw.\mathrm{}$ By extrapolating $d\Gamma /dw$ to $w=1,$ the kinematic end point at which the $D^{*}$ is at rest relative to the B, we extract the product $|V_{\mathrm{cb}}|\mathcal{F}\mathrm{}\left(1\right),$ where $\mathcal{F}\mathrm{}\left(1\right)\mathrm{}$ is the form factor at $w=1.\mathrm{}$ We find $|V_{\mathrm{cb}}|\mathcal{F}\mathrm{}\left(1\right)=0.0431\mathrm{}\pm 0.0013\left(\mathrm{stat}\right)\pm 0.0018\left(\mathrm{syst}\right).\mathrm{}$ We combine $|V_{\mathrm{cb}}|\mathcal{F}\mathrm{}\left(1\right)\mathrm{}$ with theoretical results for $\mathcal{F}\mathrm{}\left(1\right)\mathrm{}$ to determine $|V_{\mathrm{cb}}|=0.0469\mathrm{}\pm 0.0014\left(\mathrm{stat}\right)\pm 0.0020\left(\mathrm{syst}\right)\pm 0.0018\left(\mathrm{theor}\right).\mathrm{}$ We also integrate the differential decay rate over w to obtain $\mathcal{B}(B^0\to D^{*+}\mathcal{l}\overline{\nu })=(6.09\mathrm{}\pm 0.19\pm 0.40)\%$ and $\mathcal{B}{(B}^{-}\to D^{*0}\mathcal{l}\overline{\nu })=(6.50\mathrm{}\pm 0.20\pm 0.43)\%.$