Simultaneous measurement of the $B^0$ meson lifetime and mixing frequency with $B^0\to D^{*-}{\mathcal{l}}^{+}{\nu }_{\mathcal{l}}$ decays

We measure the $B^0$ lifetime ${\tau }_{B^0}$ and the $B^0-B^0$ oscillation frequency $\Delta m_d$ with a sample of approximately 14000 exclusively reconstructed $B^0\to D^{*-}{\mathcal{l}}^{+}{\nu }_{\mathcal{l}}$ signal events, selected from 23 million $B\overline{B}$ pairs recorded at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance with the BABAR detector at the Stanford Linear Accelerator Center. The decay position of the other B is determined with the remaining tracks in the event, and its b-quark flavor at the time of decay is determined with a tagging algorithm that exploits the correlation between the flavor of the b quark and the charges of its decay products. The lifetime and oscillation frequencies are measured simultaneously with an unbinned maximum-likelihood fit that uses, for each event, the measured difference in decay times of the two B mesons $\left(\Delta t\right),$ the calculated uncertainty on $\Delta t,$ the signal and background probabilities, and b-quark tagging information for the other B. The results are ${\tau }_{B^0}{=(1.523\mathrm{}}_{-0.023}^{+0.024\mathrm{}}\pm 0.022)\mathrm{ps}$ and $\Delta m_d=(0.492\mathrm{}\pm 0.018\pm 0.013){\mathrm{ps}}^{-1}.$ The statistical correlation coefficient between ${\tau }_{B^0}$ and $\Delta m_d$ is -0.22.