Dalitz plot analysis of $B^{-}\to D^{+}{\pi }^{-}{\pi }^{-}$

We report on a Dalitz plot analysis of $B^{-}\to D^{+}{\pi }^{-}{\pi }^{-}$ decays, based on a sample of about $383\times {10}^6$ ${\rm Y}(4\mathrm{S})\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ Factory at SLAC. We find the total branching fraction of the three-body decay: $\mathcal{B}(B^{-}\to D^{+}{\pi }^{-}{\pi }^{-})=(1.08\pm 0.03\pm 0.05)\times {10}^{-3}$. We observe the established $D_2^{*0}$ and confirm the existence of $D_0^{*0}$ in their decays to $D^{+}{\pi }^{-}$, where the $D_2^{*0}$ and $D_0^{*0}$ are the $2^{+}$ and $0^{+}c\overline{u}$ $P$-wave states, respectively. We measure the masses and widths of $D_2^{*0}$ and $D_0^{*0}$ to be: $m_{D_2^{*0}}=(2460.4\pm 1.2\pm 1.2\pm 1.9)\mathrm{MeV}/c^2$, ${\Gamma }_{D_2^{*0}}=(41.8\pm 2.5\pm 2.1\pm 2.0)\mathrm{MeV}$, $m_{D_0^{*0}}=(2297\pm 8\pm 5\pm 19)\mathrm{MeV}/c^2$, and ${\Gamma }_{D_0^{*0}}=(273\pm 12\pm 17\pm 45)\mathrm{MeV}$. The stated errors reflect the statistical and systematic uncertainties, and the uncertainty related to the assumed composition of signal events and the theoretical model.

Figure 1

Mass spectrum for $c\overline{u}$ states. The vertical bars show the widths. Masses and widths are from Ref. [5]. The dotted and dashed lines between the levels show the dominant pion transitions. Although it is not indicated in the figure, the two $1^{+}$ states may be mixtures of $j=1/2$ and $j=3/2$, and $D_1^{\prime }$ may decay via a $D$-wave and $D_1$ may decay via an $S$-wave.

Figure 2

$K^{+}{\pi }^{-}{\pi }^{-}$ invariant mass distribution for $D^{+}$ candidates for the selected $B^{-}\to D^{+}{\pi }^{-}{\pi }^{-}$ decays without the cut on the mass of $D^{+}$. Data (points with statistical errors) are compared to the results of the fit (solid curve), with the background distribution marked as a dashed line. The shaded area marks the $D^{+}$ signal region.

Figure 3

(a) $m_{\mathrm{ES}}$ and (b) $\Delta E$ distributions for $D^{+}{\pi }^{-}{\pi }^{-}$ candidates. Data (points with statistical errors) are compared to the results of the fits (solid curves), with the background contributions marked as dashed lines. The histograms are the corresponding distributions of the background MC sample as described in the text. The shaded area in (a) shows the signal region, while the three shaded areas in (b) mark the signal region in the center and the two sidebands.

Figure 4

Two-dimensional histogram $\cos \theta$ versus $m^2(D\pi )$ of the truth-matched events as defined in the text.

Figure 5

Two-dimensional histogram $\cos \theta$ versus $m^2(D\pi )$ of the self-crossfeed events as defined in the text.

Figure 6

$f_{\mathrm{SCF}}(\cos \theta )$ distribution. The observed self-crossfeed fractions (points with statistical errors) are compared to the results of the fit (solid curve).

Figure 7

The efficiency for signal decays as a function of $m^2(D\pi )$, as determined by MC simulation (points with statistical errors) and the results of the fit to the accepted and generated distributions (solid curve).

Figure 8

Comparison of events in the $\Delta E$ sideband: Dalitz plot for (a) data and (b) MC-simulated events, and projections on (c) $m_{\min }^2(D\pi )$, (d) $m_{\max }^2(D\pi )$, and (e) $m^2(\pi \pi )$ with data (points with statistical errors) and MC predictions (histograms).

Figure 9

Fit to background events in the $\Delta E$ signal region of the MC sample: (a) Dalitz plot and projections on (b) $m_{\min }^2(D\pi )$, (c) $m_{\max }^2(D\pi )$, and (d) $m^2(\pi \pi )$ with MC predictions (points with statistical errors) and the fits (solid curves).

Figure 10

Data Dalitz plot for $B^{-}\to D^{+}{\pi }^{-}{\pi }^{-}$.

Figure 11

Result of the nominal fit to the data: projections on (a) $m_{\min }^2(D\pi )$, (b) $m_{\max }^2(D\pi )$, and (c) $m^2(\pi \pi )$. The points with error bars are data, the solid curves represent the nominal fit. The shaded areas show the $D_2^{*0}$ contribution, the dashed curves show the $D_0^{*0}$ signal, the dash-dotted curves show the $D_v^{*}$ and $B_v^{*}$ signals, and the dotted curves show the background.

Figure 12

Result of the nominal fit to the data: the $\cos \theta$ distributions for (a) $4.5<m^2(D\pi )<5.5{\mathrm{GeV}}^2/c^4$ region and (b) $5.9<m^2(D\pi )<6.2{\mathrm{GeV}}^2/c^4$ region. The points with error bars are data, the solid curves represent the nominal fit. The dashed, dash-dotted, and dotted curves in (a) show the fit of hypotheses 2–4 in Table 3, respectively. The shaded histograms show the $\cos \theta$ distributions from $\Delta E$ sidebands in data.