$B^0$ meson decays to ${\rho }^0{K}^{*0}$, $f_0{K}^{*0}$, and ${\rho }^{-}{K}^{*+}$, including higher $K^{*}$ resonances

We present branching fraction measurements for the decays $B^0\to {\rho }^0{K}^{*0}$, $B^0\to f_0{K}^{*0}$, and $B^0\to {\rho }^{-}{K}^{*+}$, where $K^{*}$ is an $S$-wave $(K\pi {)}_0^{*}$ or a $K^{*}(892)$ meson; we also measure $B^0\to f_0{K}_2^{*}(1430{)}^0$. For the $K^{*}(892)$ channels, we report measurements of longitudinal polarization fractions (for $\rho$ final states) and direct $CP$ violation asymmetries. These results are obtained from a sample of $(471.0\pm 2.8)\times {10}^6$ $B\overline{B}$ pairs collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at the SLAC National Accelerator Laboratory. We observe ${\rho }^0{K}^{*}(892{)}^0$, ${\rho }^0(K\pi {)}_0^{*0}$, $f_0{K}^{*}(892{)}^0$, and ${\rho }^{-}{K}^{*}(892{)}^{+}$ with greater than $5\sigma$ significance, including systematics. We report first evidence for $f_0(K\pi {)}_0^{*0}$ and $f_0{K}_2^{*}(1430{)}^0$, and place an upper limit on ${\rho }^{-}(K\pi {)}_0^{*+}$. Our results in the $K^{*}(892)$ channels are consistent with no direct $CP$ violation.

Figure 1

Feynman diagrams for (a–b) $B^0\to {\rho }^0{K}^{*0}$ and (c–d) $B^0\to {\rho }^{-}{K}^{*+}$. Gluonic penguin diagrams (a, c) dominate over tree (b, d) contributions.

Figure 2

Definition of the helicity angles for $B^0\to {\rho }^0{K}^{*0}$.

Figure 3

(color online) ${\pi }^{+}{\pi }^{-}$ mass spectrum for sWeighted $K^{*}(892{)}^0$ events. The solid curve is the fit function, the [green] dotted curve is ${\rho }^0$, [red] dash-dotted curve is $f_0$, and [blue] dashed curve is $f_2(1270)$.

Figure 4

(color online) $B$ candidate $m_{\mathrm{ES}}$ projections for (a) ${\rho }^0/f_0{K}^{*}(892{)}^0$ (b) inclusive $(K\pi {)}_0^{*0}$ and $K_2^{*}(1430{)}^0$, (c) ${\rho }^{-}{K}^{*}(892{)}^{+}$, (d) ${\rho }^{-}(K\pi {)}_0^{*+}$ and ${\rho }^{-}{K}_2^{*}(1430{)}^{+}$. The solid curve is the fit function, [black] long-dash–dotted curve is the total background, and the [blue] dashed curve is the total signal contribution. In (a), we separate the [red] dashed ${\rho }^0$ component from the [green] dotted $f_0$. In (b) and (d), $(K\pi {)}_0^{*}$ signal is [green] dotted and $K_2^{*}(1430)$ is [red] dashed. In (b), the two-stage nature of the fit means that the $(K\pi {)}_0^{*0}$ and $K_2^{*}(1430{)}^0$ signals include both $f_0$ and ${\rho }^0$ components, as the first stage of the HMR fit does not include information about the ${\pi }^{+}{\pi }^{-}$ mass spectrum.

Figure 5

(color online) Invariant mass projections for LMR (a, c) ${\rho }^0/f_0{K}^{*}(892{)}^0$ and (b, d) ${\rho }^{-}{K}^{*}(892{)}^{+}$; $\pi \pi$ mass (left) and $K\pi$ mass (right). The solid curve is the fit function, [black] long-dash–dotted curve is the total background, and the [blue] dashed curve is the total signal contribution. In (a), we separate the [red] dashed ${\rho }^0$ component from the [green] dotted $f_0$. In (c) and (d), $(K\pi {)}_0^{*}$ background is [green] dotted.

Figure 6

(color online) Invariant mass projections for HMR ${\rho }^0(K\pi {)}_0^{*0}$, $f_0(K\pi {)}_0^{*0}$, and $f_0{K}_2^{*}(1430{)}^0$ signals (a) $K^{+}{\pi }^{-}$ mass, (b) ${\pi }^{+}{\pi }^{-}$ mass for sWeighted $(K\pi {)}_0^{*0}$ events, (c) ${\pi }^{+}{\pi }^{-}$ mass for sWeighted $K_2^{*}(1430{)}^0$ events. The solid curve is the fit function. In (a), the [black] long-dash–dotted curve is the total background, the [blue] dashed curve is the total signal contribution, the [green] dotted curve is the $(K\pi {)}_0^{*0}$ component, and the [red] dashed curve is $K_2^{*}(1430{)}^0$. In (b) and (c), the ${\rho }^0$ component is the [red] dashed curve and $f_0$ is the [blue] long-dashed curve.