Study of $D^{**}$ production and light hadronic states in the ${\overline{B}}^0\to D^{*+}\omega {\pi }^{-}$ decay

We report on the first observations of ${\overline{B}}^0\to D_1(2430{)}^0\omega$, ${\overline{B}}^0\to D_1(2420{)}^0\omega$, and ${\overline{B}}^0\to D_2^{*}(2460{)}^0\omega$ decays. The ${\overline{B}}^0\to D^{*+}\rho (1450{)}^{-}$ decay is also observed. The branching fraction measurements are based on $(771.6\pm 10.6)\times {10}^6$ $B\overline{B}$ events collected at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The fractions of longitudinal polarization of the $D^{**}$ states as well as partial wave fractions of the $D_1(2430{)}^0$ are obtained. We also set a 90% confidence level upper limit for the product of branching fractions of $\mathcal{B}({\overline{B}}^0\to D^{*+}{b}_1(1235{)}^{-})\times \mathcal{B}(b_1(1235{)}^{-}\to \omega {\pi }^{-})$. The measurements show evidence of nontrivial final-state interaction phases for the $\rho$-meson-like amplitudes.

Figure 1

(a) Color-suppressed and (b) color-favored tree diagrams for the production of $D^{**}$ and $\omega \pi$ states in ${\overline{B}}^0\to D^{*+}\omega {\pi }^{-}$ decays, respectively.

Figure 2

Simulated $(X,Y)$ Dalitz distribution of the $\omega$ signal events. The curve bounds the area selected for further study.

Figure 3

Distribution of $\mathrm{\Delta }E$ versus $M({\pi }^{+}{\pi }^{-}{\pi }^0)$ for the selected ${\overline{B}}^0\to D^{*+}\omega {\pi }^{-}$ candidates. The signal Region (I) and sideband Regions (II, III and IV) are shown. A clear correlation between the variables is seen in Region I.

Figure 4

$M({\pi }^{-}{\pi }^{+}{\pi }^0$) distribution of the ${\overline{B}}^0\to D^{*+}\omega {\pi }^{-}$ candidates in the $\mathrm{\Delta }E$ signal region (points with error bars) and sideband (hatched histogram). The sideband distribution is normalized to the size of the $\mathrm{\Delta }E$ signal region. The $M({\pi }^{+}{\pi }^{-}{\pi }^0)$ signal region and sideband are indicated by the vertical lines. The curve is the result of the fit described in the text.

Figure 5

$\mathrm{\Delta }E$ distributions of the ${\overline{B}}^0\to D^{*+}\omega {\pi }^{-}$ candidates in the (a) signal and (b) sideband regions of $M({\pi }^{+}{\pi }^{-}{\pi }^0)$. The hatched histogram in (a) represents the $M({\pi }^{+}{\pi }^{-}{\pi }^0)$ sideband normalized to the size of the signal region. The $\mathrm{\Delta }E$ signal region and sideband are indicated by the vertical lines. The curves are the results of the fit described in the text.

Figure 6

Kinematics of a ${\overline{B}}^0\to D^{*+}\omega {\pi }^{-}$ decay mediated by an $\omega {\pi }^{-}$ intermediate resonance. The diagram in (a) defines two polar angles ${\xi }_1$ and ${\beta }_1$ and one azimuthal angle ${\psi }_1$. The diagram in (b) defines one polar angle ${\theta }_1$ and one azimuthal angle ${\varphi }_1$. The direction $n_{\omega }$ in (b) corresponds to the vector normal to the $\omega$ decay plane.

Figure 7

$M^2(\omega \pi )$ and $M^2(D^{*}\pi )$ distributions of the ${\overline{B}}^0\to D^{*+}\omega {\pi }^{-}$ candidates in the $(\mathrm{\Delta }E,M({\pi }^{+}{\pi }^{-}{\pi }^0))$ sideband regions (a,b) IV, (c,d) III and (e,f) II. Points with error bars are data; hatched histograms correspond to the contribution from $B_{\mathrm{IV}}(\overrightarrow{x})$; dotted histograms represent the component described by the function $B_{\mathrm{III}}(\overrightarrow{x})$ in (c) and (d) and $B_{\mathrm{II}}(\overrightarrow{x})$ in (e) and (f); open histograms correspond to the total fit results in Regions III and II.

Figure 8

(a) $M^2(\omega \pi )$ and (b) $M^2(D^{*}\pi )$ distributions of the background components in the signal region. The histograms are stacked on top of each other.

Figure 9

Dalitz distributions of the $D^{*+}\omega {\pi }^{-}$ candidates in (a) signal Region I, (b) sideband Region II, (c) sideband Region III and (d) sideband Region IV.

Figure 10

Distribution of the six $\mathit{\omega }\mathit{\pi }$ variables for $D^{*}\omega \pi$ candidates in the signal region (points with error bars). The histograms represent the results of the fit (black), including the following components: $\rho (770)$ (cyan), $\rho (1450)$ (red), $\rho (770)$ and $\rho (1450)$ together (red dashed), $D_1(2430{)}^0$ (green), $D_1(2420{)}^0$ (blue), $D_2^{*}(2460{)}^0$ (magenta) and background (hatched).

Figure 11

Distribution of the six ${\mathit{D}}^{*}\mathit{\pi }$ variables for $D^{*}\omega \pi$ candidates in the signal region (points with error bars). The histograms represent the results of the fit (black), including the following components: $\rho (770)$ (cyan), $\rho (1450)$ (red), $\rho (770)$ and $\rho (1450)$ together (red dashed), $D_1(2430{)}^0$ (green), $D_1(2420{)}^0$ (blue), $D_2^{*}(2460{)}^0$ (magenta) and background (hatched).

Figure 12

Distribution of three $\mathit{\omega }\mathit{\pi }$ variables for $D^{*+}\omega {\pi }^{-}$ candidates in two different subregions of the signal region (points with error bars), defined by $\cos {\xi }_2>-0.4$ or $|\cos {\theta }_1|>0.5$ ($D^{**}$ enriched) and $|\cos {\theta }_1|<0.5$ ($D^{**}$ depleted). The histograms represent the results of the fit (black), including the following components: $\rho (770)$ (cyan), $\rho (1450)$ (red), $\rho (770)$ and $\rho (1450)$ together (red dashed), $D_1(2430{)}^0$ (green), $D_1(2420{)}^0$ (blue), $D_2^{*}(2460{)}^0$ (magenta) and background (hatched).

Figure 13

Distribution of three ${\mathit{D}}^{*}\mathit{\pi }$ variables for $D^{*+}\omega {\pi }^{-}$ candidates in two different subregions of the signal region (points with error bars), defined by $\cos {\xi }_2>-0.4$ ($D^{**}$ enriched) and $|\cos {\theta }_1|<0.5$ ($D^{**}$ depleted). The histograms represent the results of the fit (black), including the following components: $\rho (770)$ (cyan), $\rho (1450)$ (red), $\rho (770)$ and $\rho (1450)$ together (red dashed), $D_1(2430{)}^0$ (green), $D_1(2420{)}^0$ (blue), $D_2^{*}(2460{)}^0$ (magenta) and background (hatched).