Time-dependent Dalitz plot analysis of $B^0\to D^{\mp }{K}^0{\pi }^{\pm }$ decays

We present for the first time a measurement of the weak phase $2\beta +\gamma$ obtained from a time-dependent Dalitz plot analysis of $B^0\to D^{\mp }{K}^0{\pi }^{\pm }$ decays. Using a sample of approximately $347\times {10}^6$ $B\overline{B}$ pairs collected by the BABAR detector at the PEP-II asymmetric-energy storage rings and assuming the ratio $r$ of the $b\to u$ and $b\to c$ decay amplitudes to be 0.3, we obtain $2\beta +\gamma =(83\pm 53\pm 20)°$ and the equivalent solution at $+180°$. The magnitudes and phases for the resonances associated with the $b\to c$ transitions are also extracted from the fit.

Figure 1

The distributions of $m^2(K_S^0\pi )$ and $m^2(D\pi )$ in data (solid points). The overall PDF is superimposed (black line). The gray full line is the signal PDF; the dashed black line is the background PDF.

Figure 2

(a) The $m_{\mathrm{ES}}$ distribution of on-resonance data (solid points) for the global fitted PDF (black line) with the contribution of the PDF for each component superimposed: signal (gray line), continuum (small dashed line), combinatoric $B\overline{B}$ (large dashed line), and Peak (dotted line). To enhance the signal $|\Delta \mathrm{E}|<0.025\mathrm{GeV}$ and $\mathcal{F}>0.2$ have been required. (b) Distribution of the values of $2\beta +\gamma$ fitted on data for different hypotheses on the $r$ value. (c) Variation of the logarithm of the likelihood with $2\beta +\gamma$.