Measurements of Branching Fractions and Dalitz Distributions for $B^0\to D^{(*)\pm }{K}^0{\pi }^{\mp }$ Decays

We present measurements of the branching fractions for the three-body decays $B^0\to D^{(*)\mp }{K}^0{\pi }^{\pm }$ and their resonant submodes $B^0\to D^{(*)\mp }{K}^{*\pm }$ using a sample of approximately $88\times {10}^6$ $B\overline{B}$ pairs collected by the BABAR detector at the SLAC PEP-II asymmetric energy storage ring. We measure: $\mathcal{B}(B^0\to D^{\mp }{K}^0{\pi }^{\pm })=(4.9\pm {0.7}_{\mathrm{stat}}\pm {0.5}_{\mathrm{syst}})\times {10}^{-4}$, $\mathcal{B}(B^0\to D^{*\mp }{K}^0{\pi }^{\pm })=(3.0\pm {0.7}_{\mathrm{stat}}\pm {0.3}_{\mathrm{syst}})\times {10}^{-4}$, $\mathcal{B}(B^0\to D^{\mp }{K}^{*\pm })=(4.6\pm {0.6}_{\mathrm{stat}}\pm {0.5}_{\mathrm{syst}})\times {10}^{-4}$, $\mathcal{B}(B^0\to D^{*\mp }{K}^{*\pm })=(3.2\pm {0.6}_{\mathrm{stat}}\pm {0.3}_{\mathrm{syst}})\times {10}^{-4}$. From these measurements we determine the fractions of resonant events to be $f(B^0\to D^{\mp }{K}^{*\pm })=0.63\pm {0.08}_{\mathrm{stat}}\pm {0.04}_{\mathrm{syst}}$ and $f(B^0\to D^{*\mp }{K}^{*\pm })=0.72\pm {0.14}_{\mathrm{stat}}\pm {0.05}_{\mathrm{syst}}$.

Figure 1

$m_{\mathrm{ES}}$ distributions in data for the four decay modes. In solid markers are shown events weighted by $W_{\mathrm{sig}}$ (see text). Following the presciption of [8] the $m_{\mathrm{ES}}$ variable was removed from the likelihood to perform the second fit needed to obtain the $m_{\mathrm{ES}}$ free yields and covariance matrix entering into $W_{\mathrm{sig}}$. The PDF used in the main fit is superimposed for comparison. For comparison, the $m_{\mathrm{ES}}$ distribution obtained with $|\Delta E|<25\mathrm{MeV}$ ($2\sigma$) is included (dotted points).

Figure 2

Signal Dalitz distributions with events weighted by $W_{\mathrm{sig}}$ and corrected for efficiency variations. Each bin is colored according to its contribution to the branching fraction. The bins in white also include the contributions which are negative but still statistically compatible with zero.

Figure 3

Distribution of $\cos \theta$ for data for the $B^0\to D^{\mp }{K}^0{\pi }^{\pm }$ decay mode in the $K^{*\pm }$ region using the signal weights $W_{\mathrm{sig}}$ and correcting for efficiency variations. The solid curve shows the expected spin-1 distribution $dN/d\cos \theta \propto {cos}^2\theta$.