Measurement of the ${\overline{B}}^0$ lifetime and the $B^0{\overline{B}}^0$ oscillation frequency using partially reconstructed ${\overline{B}}^0\to D^{*+}{\ell }^{-}{\overline{\nu }}_{\ell }$ decays

We present a simultaneous measurement of the ${\overline{B}}^0$ lifetime ${\tau }_{B^0}$ and $B^0{\overline{B}}^0$ oscillation frequency $\Delta m_d$. We use a sample of about 50 000 partially reconstructed ${\overline{B}}^0\to D^{*+}{\ell }^{-}{\overline{\nu }}_{\ell }$ decays identified with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ storage ring at SLAC. The flavor of the other $B$ meson in the event is determined from the charge of another high-momentum lepton. The results are ${\tau }_{B^0}=(1.504\pm 0.013{(\mathrm{stat})}_{-0.013}^{+0.018}(\mathrm{syst}))\mathrm{ps}$, $\Delta m_d=(0.511\pm 0.007{(\mathrm{stat})}_{-0.006}^{+0.007}{(\mathrm{syst}))\mathrm{ps}}^{-1}$.

Figure 1

${\mathcal{M}}_{\nu }^2$ distribution for right-charge (top) and wrong-charge (bottom) events. The points correspond to on-resonance data. The distributions of continuum events (dark histogram), obtained from luminosity-rescaled off-resonance events, and $B\overline{B}$ combinatorial background events (hatched area), obtained from the simulation, are overlaid. Monte Carlo events are normalized to the difference between on-peak and rescaled off-peak data in the region ${\mathcal{M}}_{\nu }^2<-4.5{\mathrm{GeV}}^2/c^4$.

Figure 2

Distribution of the combined signal likelihood $\mathcal{X}$ for events in the signal ${\mathcal{M}}_{\nu }^2$ region. Events for which $\mathcal{X}<0.4$ are rejected.

Figure 3

Fit to the ${\mathcal{M}}_{\nu }^2$ distribution for the unmixed events (a) and mixed events (b). “${\overline{B}}^0$” includes ${\overline{B}}^0\to D^{*+}{\ell }^{-}{\overline{\nu }}_{\ell }$, ${\overline{B}}^0\to D^{*+}{\pi }^0{\ell }^{-}{\overline{\nu }}_{\ell }$, ${\overline{B}}^0\to D^{*+}{\tau }^{-}{\overline{\nu }}_{\tau }$ ($\tau \to \ell X$), ${\overline{B}}^0\to D^{*+}{D}_s^{-}$ ($D_s\to \ell X$), ${\overline{B}}^0\to D^{*+}\overline{D}X$ ($\overline{D}\to \ell Y$), and ${\overline{B}}^0\to D^{*+}h$ with the hadron $h$ misidentified as a muon. “$B^{-}$” includes $B^{-}\to D^{*+}{\pi }^{-}{\ell }^{-}{\overline{\nu }}_{\ell }$ and $B^{-}\to D^{*+}{\pi }^{-}X$ with the ${\pi }^{-}$ misidentified as a muon. “Other” includes $B\to D^{*}\pi {\nu }_{\tau }\tau$ ($\tau \to \ell X$), $B\to D^{*}\pi \overline{D}X$ ($\overline{D}\to \ell Y$).

Figure 4

Fraction of continuum events, peaking $B^{-}$, and $B\overline{B}$ combinatorial background in the unmixed (a) and mixed (b) lepton-tagged samples. The continuous lines overlaid represent the analytic functions ($f_{qq}^{\pm },f_{B^{-}}^{\pm }$ and $f_{B\overline{B}}^{\pm }$) used to parametrize the distributions. The fraction of continuum events is parametrized only in the region ${\mathcal{M}}_{\nu }^2>-4.5{\mathrm{GeV}}^2/c^4$. For ${\mathcal{M}}_{\nu }^2<-4.5{\mathrm{GeV}}^2/c^4$, where just continuum and combinatorial backgrounds are present, we assume that $f_{B^{-}}^{\pm }=0$, and we compute $f_{qq}^{\pm }=1-f_{B\overline{B}}^{\pm }$.

Figure 5

Distribution of $\cos {\theta }_{{\pi }_s^{+}{\ell }^{-}}$ for unmixed events. In (a), the points with error bars represent the data, and the histograms show the various sample components determined by the fit; (b) shows the ratio between the fraction of tags from $D^0$ decays over the total number of tags in signal events, as obtained from the simulation rescaled to the result of the fit. This distribution is parametrized by a third-order polynomial represented by the continuous line overlaid. The dotted line represents the corresponding distribution obtained without rescaling the simulation to the fit result.

Figure 6

Same as Fig. 5 for mixed events.

Figure 7

Distribution of $\Delta t$ for unmixed (a) and mixed (b) events in the signal ${\mathcal{M}}_{\nu }^2$ region. The points show the data, the curve is the projection of the fit result, and the shaded areas from bottom to top are the contributions from continuum background, $B\overline{B}$ combinatorial background, peaking $B^{-}$ background with decay-side tag, peaking $B^{-}$ background with primary tag, signal with decay-side tag, signal with cascade tag, and signal with primary tag.

Figure 8

Same as Fig. 7 with logarithmic scale.

Figure 9

Distribution of $\Delta t$ for unmixed (a) and mixed (b) events in the background ${\mathcal{M}}_{\nu }^2$ region. The points show the data, the curve is the projection of the fit result, and the shaded areas are the contributions from continuum and $B\overline{B}$ combinatorial background.

Figure 10

Same as Fig. 9 with logarithmic scale.

Figure 11

Asymmetry between unmixed and mixed events as a function of $\Delta t$, for events in the signal ${\mathcal{M}}_{\nu }^2$ region. Points with error bars represent the data, and the curve is a projection of the fit result.

Figure 12

Asymmetry between unmixed and mixed events as a function of $\Delta t$, for events in the background ${\mathcal{M}}_{\nu }^2$ region. Points with error bars represent the data, and the curve is a projection of the fit result.