Branching Fractions and $CP$ Asymmetries in $B^0\to {\pi }^0{\pi }^0$, $B^{+}\to {\pi }^{+}{\pi }^0$, and $B^{+}\to K^{+}{\pi }^0$ Decays and Isospin Analysis of the $B\to \pi \pi$ System

Based on a sample of $227\times {10}^6$ $B\overline{B}$ pairs collected by the BABAR detector at the PEP-II asymmetric-energy $B$ Factory at SLAC, we measure the branching fraction $\mathcal{B}(B^0\to {\pi }^0{\pi }^0)=(1.17\pm 0.32\pm 0.10)\times {10}^{-6}$, and the asymmetry $C_{{\pi }^0{\pi }^0}=-0.12\pm 0.56\pm 0.06$. The $B^0\to {\pi }^0{\pi }^0$ signal has a significance of $5.0\sigma$. We also measure $\mathcal{B}(B^{+}\to {\pi }^{+}{\pi }^0)=(5.8\pm 0.6\pm 0.4)\times {10}^{-6}$, $\mathcal{B}(B^{+}\to K^{+}{\pi }^0)=(12.0\pm 0.7\pm 0.6)\times {10}^{-6}$, and the charge asymmetries ${\mathcal{A}}_{{\pi }^{+}{\pi }^0}=-0.01\pm 0.10\pm 0.02$ and ${\mathcal{A}}_{K^{+}{\pi }^0}=0.06\pm 0.06\pm 0.01$. Using isospin relations, we find an upper bound on the angle difference $|\alpha -{\alpha }_{\mathrm{eff}}|$ of 35° at the 90% C.L.

Figure 1

Distributions and PDF projections for $B^0\to {\pi }^0{\pi }^0$. Shown are (a) $m_{\mathrm{ES}}$, (b) $F$, and (c) $\Delta E$ for candidates that satisfy an optimized requirement on the signal probability, based on all variables except the one being plotted. The three projections contain, respectively, 25%, 68%, 45% of the signal, 14%, 17%, 31% of the ${\rho }^{+}{\pi }^0$ background, and 2.2%, 4.4%, 1.3% of the continuum background. For (d) the requirement is loosened to include 80% of the signal. PDF projections are shown as a dashed line for $q\overline{q}$ background, a dotted line for $B$ background, and a dash-dotted line for signal.

Figure 2

Distributions and PDF projections for $B^{+}\to h^{+}{\pi }^0$, using the method described in the text. For $m_{\mathrm{ES}}$ (a) the signal distributions are combined, while for $\Delta E$ (b) the signal $B^{+}\to {\pi }^{+}{\pi }^0$ (open circles and dash-dotted curve) and $B^{+}\to K^{+}{\pi }^0$ (solid circles and curve) are shown separately. The insets show the combined background components.

Figure 3

Constraints on the $|\Delta {\alpha }_{\pi \pi }|$ in terms of confidence level. We find an upper bound on $|\Delta {\alpha }_{\pi \pi }|$ of 35° at the 90% C.L.