Measurement of Branching Fractions and Charge Asymmetries in $B^{\pm }\to {\rho }^{\pm }{\pi }^0$ and $B^{\pm }\to {\rho }^0{\pi }^{\pm }$ Decays, and Search for $B^0\to {\rho }^0{\pi }^0$

We present measurements of branching fractions and charge asymmetries in $B$-meson decays to ${\rho }^{+}{\pi }^0$, ${\rho }^0{\pi }^{+}$, and ${\rho }^0{\pi }^0$. The data sample comprises $89\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ Factory at SLAC. We find the charge-averaged branching fractions $\mathcal{B}(B^{+}\to {\rho }^{+}{\pi }^0)=[10.9\pm 1.9\mathrm{(}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{)}\pm 1.9\mathrm{(}\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{)}]\times {10}^{-6}$ and $\mathcal{B}(B^{+}\to {\rho }^0{\pi }^{+})=(9.5\pm 1.1\pm 0.9)\times {10}^{-6}$, and we set a $90\%$ confidence-level upper limit $\mathcal{B}(B^0\to {\rho }^0{\pi }^0)<2.9\times {10}^{-6}$. We measure the charge asymmetries $A_{CP}^{{\rho }^{+}{\pi }^0}=0.24\pm 0.16\pm 0.06$ and $A_{CP}^{{\rho }^0{\pi }^{+}}=-0.19\pm 0.11\pm 0.02$.

Figure 1

Distributions of $m_{ES}$ and $\Delta E$ for samples enhanced in ${\rho }^0{\pi }^{+}$ signal (a),(b), ${\rho }^{+}{\pi }^0$ signal (c),(d), and ${\rho }^0{\pi }^0$ signal (e),(f). The solid curve represents a projection of the maximum likelihood fit result. The dashed curve represents the contribution from continuum events, and the dotted line indicates the combined contributions from continuum events and $B$-related backgrounds.

Figure 2

Distributions of $\rho$ mass and helicity for samples enhanced in ${\rho }^0{\pi }^{+}$ signal (a),(b) with the same line conventions used in Fig. 1.