Measurements of branching fractions, polarizations, and direct $CP$-violation asymmetries in $B^{+}\to {\rho }^0{K}^{*+}$ and $B^{+}\to f_0(980)K^{*+}$ decays

We present measurements of the branching fractions, longitudinal polarization, and direct $CP$-violation asymmetries for the decays $B^{+}\to {\rho }^0{K}^{*+}$ and $B^{+}\to f_0(980)K^{*+}$ with a sample of $(467\pm 5)\times {10}^{6}B\overline{B}$ pairs collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at the SLAC National Accelerator Laboratory. We observe $B^{+}\to {\rho }^0{K}^{*+}$ with a significance of $5.3\sigma$ and measure the branching fraction $\mathcal{B}(B^{+}\to {\rho }^0{K}^{*+})=(4.6\pm 1.0\pm 0.4)\times {10}^{-6}$, the longitudinal polarization $f_L=0.78\pm 0.12\pm 0.03$, and the $CP$-violation asymmetry ${\mathcal{A}}_{CP}=0.31\pm 0.13\pm 0.03$. We observe $B^{+}\to f_0(980)K^{*+}$ and measure the branching fraction $\mathcal{B}(B^{+}\to f_0(980)K^{*+})\times \mathcal{B}(f_0(980)\to {\pi }^{+}{\pi }^{-})=(4.2\pm 0.6\pm 0.3)\times {10}^{-6}$ and the $CP$-violation asymmetry ${\mathcal{A}}_{CP}=-0.15\pm 0.12\pm 0.03$. The first uncertainty quoted is statistical and the second is systematic.

Figure 1

Projections of the multidimensional fit onto (a) $m_{\mathrm{ES}}$, (b) $\Delta E$, (c) ${\pi }^{+}{\pi }^{-}$ mass, (d) $K_S^0{\pi }^{+}$ mass, (e) $|\cos {\theta }_{{\pi }^{+}{\pi }^{-}}|$, and (f) $\cos {\theta }_{K_S^0{\pi }^{+}}$ for modes with $K^{*+}\to K_S^0{\pi }^{+}$. The points with error bars show the data; the solid line shows signal-plus-background; the hatched [green] area is the ${\rho }^0{K}^{*+}$ signal; and the dashed [red] line is the $f_0(980)K^{*+}$ signal.

Figure 2

Projections of the multidimensional fit onto (a) $m_{\mathrm{ES}}$, (b) $\Delta E$, (c) ${\pi }^{+}{\pi }^{-}$ mass, (d) $K^{+}{\pi }^0$ mass, (e) $|\cos {\theta }_{{\pi }^{+}{\pi }^{-}}|$, and (f) $\cos {\theta }_{K^{+}{\pi }^0}$ for modes with $K^{*+}\to K^{+}{\pi }^0$. The figure uses the same projection criteria and legend as Fig. 1.