Observation of the Decay $B^{\pm }\to {\pi }^{\pm }{\pi }^0$, Study of $B^{\pm }\to K^{\pm }{\pi }^0$, and Search for $B^0\to {\pi }^0{\pi }^0$

We present results for the branching fractions and charge asymmetries in $B^{\pm }\to h^{\pm }{\pi }^0$ (where $h^{\pm }={\pi }^{\pm },K^{\pm }$) and a search for the decay $B^0\to {\pi }^0{\pi }^0$ using a sample of approximately $88\times {10}^6$ $B\overline{B}$ pairs collected by the BABAR detector at the PEP-II asymmetric-energy $B$ Factory at SLAC. We measure $\mathcal{B}(B^{\pm }\to {\pi }^{\pm }{\pi }^0)=({5.5}_{-0.9}^{+1.0}\pm 0.6)\times {10}^{-6}$, where the first error is statistical and the second is systematic. The $B^{\pm }\to {\pi }^{\pm }{\pi }^0$ signal has a significance of $7.7\sigma$ including systematic uncertainties. We simultaneously measure the $K^{\pm }{\pi }^0$ branching fraction to be $\mathcal{B}(B^{\pm }\to K^{\pm }{\pi }^0)=({12.8}_{-1.1}^{+1.2}\pm 1.0)\times {10}^{-6}$. The charge asymmetries are ${\mathcal{A}}_{{\pi }^{\pm }{\pi }^0}=-{0.03}_{-0.17}^{+0.18}\pm 0.02$ and ${\mathcal{A}}_{K^{\pm }{\pi }^0}=-0.09\pm 0.09\pm 0.01$. We place a 90% confidence-level upper limit on the branching fraction $\mathcal{B}(B^0\to {\pi }^0{\pi }^0)$ of $3.6\times {10}^{-6}$.

Figure 1

The distributions of $m_{\mathrm{E}\mathrm{S}}$ (left panels) and $\Delta E$ (right panels) for $B^{\pm }\to {\pi }^{\pm }{\pi }^0$ (top panels) and $B^{\pm }\to K^{\pm }{\pi }^0$ (bottom panels), for candidates that satisfy optimized requirements on probability ratios for signal to background based on all variables except the one being plotted. The fraction of signal events included in the plots is 24% ($m_{\mathrm{E}\mathrm{S}}$) and 35% ($\Delta E$) for ${\pi }^{\pm }{\pi }^0$, and 53% ($m_{\mathrm{E}\mathrm{S}}$) and 48% ($\Delta E$) for $K^{\pm }{\pi }^0$. Solid curves represent projections of the complete maximum likelihood fit result; dashed curves represent the background contribution. For the $B^{\pm }\to {\pi }^{\pm }{\pi }^0$ $\Delta E$ distribution, the dotted curve shows the $q\overline{q}$ background and the small $B^{\pm }\to K^{\pm }{\pi }^0$ cross feed; the dashed curve includes the $B\to \rho \pi$ background as well, so is the sum of all backgrounds.

Figure 2

The (a) $m_{\mathrm{E}\mathrm{S}}$, (b) $\Delta E$, and (c) ${\mathcal{F}}_{\mathcal{T}}$ distributions for $B^0\to {\pi }^0{\pi }^0$ are shown, for candidates that satisfy optimized requirements on probability ratios for signal to background based on all variables except the one being plotted. The fractions of signal events included in the plots are 20%, 20%, and 63% for $m_{\mathrm{E}\mathrm{S}}$, $\Delta E$ and ${\mathcal{F}}_{\mathcal{T}}$, respectively. The dashed lines show the PDF projections for both $q\overline{q}$ and $B^{\pm }\to {\rho }^{\pm }{\pi }^0$ background, while the solid lines are the PDF projections for signal plus background. The ratio $-2\ln (\mathcal{L}/{\mathcal{L}}_{\max })$ is shown in (d), where the dashed line is for statistical errors only and the solid line is for statistical and systematic errors, as applied for the calculation of significance.