Measurement of time-dependent $CP$-violating asymmetries and constraints on $\sin (2\beta +\gamma )$ with partial reconstruction of $B\to D^{*\mp }{\pi }^{\pm }$ decays

We present a measurement of the time-dependent $CP$-violating asymmetries in decays of neutral $B$ mesons to the final states $D^{*\mp }{\pi }^{\pm }$, using approximately $232\times {10}^6$ $B\overline{B}$ events recorded by the BABAR experiment at the PEP-II $e^{+}{e}^{-}$ storage ring. Events containing these decays are selected with a partial reconstruction technique, in which only the high-momentum ${\pi }^{\pm }$ from the $B$ decay and the low-momentum ${\pi }^{\mp }$ from the $D^{*\mp }$ decay are used. We measure the parameters related to $2\beta +\gamma$ to be $a_{D^{*}\pi }=-0.034\pm 0.014\pm 0.009$ and $c_{D^{*}\pi }^{\ell }=-0.019\pm 0.022\pm 0.013$. With some theoretical assumptions, we interpret our results in terms of the lower limits $|\sin (2\beta +\gamma )|>0.62(0.35)$ at 68% (90%) confidence level.

Figure 1

Feynman diagrams for the Cabibbo-favored decay $B^0\to D^{*-}{\pi }^{+}$ (left), corresponding to the decay amplitude $A_c$, and the Cabibbo-suppressed decay ${\overline{B}}^0\to D^{*-}{\pi }^{+}$ (right), whose amplitude is $A_u$.

Figure 2

Momenta and angles in the CM frame used in the partial reconstruction. The orthogonal axes $u$ and $v$ are normal to the momentum ${\overrightarrow{p}}_h$ of the fast pion, and $u$ lies in the plane defined by the momenta of the fast and slow pions, ${\overrightarrow{p}}_h$ and ${\overrightarrow{p}}_s$. The angle $\varphi$ is measured in the $u-v$ plane.

Figure 3

The $m_{\mathrm{miss}}$ distributions for on-resonance lepton-tagged (top) and kaon-tagged (bottom) data. The curves show, from bottom to top, the cumulative contributions of the continuum, peaking $B\overline{B}$, combinatoric $B\overline{B}$, $B\to D^{*\mp }{\rho }^{\pm }$, and $B\to D^{*\mp }{\pi }^{\pm }$ PDF components.

Figure 4

The $F$ distributions for on-resonance lepton-tagged (top) and kaon-tagged (bottom) data. The contributions of the $B\overline{B}$ (dashed-dotted line) and the continuum (dashed line) PDF components are overlaid, peaking at approximately $-0.6$ and $-0.1$, respectively. The total PDF is also overlaid.

Figure 5

$\Delta t$ distributions for the lepton-tagged (a-d) and kaon-tagged (e-h) events separated according to the tagged flavor of $B_{\mathrm{tag}}$ and whether they were found to be mixed or unmixed: a,e) $B^0$ unmixed, b,f) ${\overline{B}}^0$ unmixed, c,g) $B^0$ mixed, d,h) ${\overline{B}}^0$ mixed. The solid curves show the PDF, calculated with the parameters obtained by the fit. The PDF for the total background is shown by the dashed curves.

Figure 6

Raw asymmetry for (a) lepton-tagged and (b) kaon-tagged events. The curves represent the projections of the PDF for the raw asymmetry. A nonzero value of $a_{D^{*}\pi }$ would show up as a sinusoidal asymmetry, up to resolution and background effects. The offset from the horizontal axis is due to the nonzero values of $\Delta {ϵ}_{D^{*}\pi }$ and $\Delta {\omega }_{D^{*}\pi }$.

Figure 7

Lower limit on $|\sin (2\beta +\gamma )|$ at 90% CL as a function of $r^{*}$, for $r^{*}>0.001$.

Figure 8

The shaded region denotes the allowed range of $|\sin (2\beta +\gamma )|$ for each confidence level. The horizontal lines show, from top to bottom, the 68% and 90% CL.

Figure 9

Contours of constant probability (color-coded in percent) for the position of the apex of the unitary triangle to be inside the contour, based on the results of Fig. 8. The cross represents the value and errors on the position of the apex of the unitarity triangle from the CKMFitter fit using the “ICHEP04” results excluding this measurement [22].