Measurement of the branching fraction and $CP$ asymmetry in $B^0\to {\pi }^0{\pi }^0$ decays, and an improved constraint on ${\varphi }_2$

We measure the branching fraction and $CP$ violation asymmetry in the decay $B^0\to {\pi }^0{\pi }^0$, using a data sample of $752\times {10}^6$ $B\bar{B}$ pairs collected at the $\mathrm{{\rm Y}}(4S)$ resonance with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. The obtained branching fraction and direct $CP$ asymmetry are $ $\mathcal{B}$(B\to \pi^{0}\pi^{0}) = [1.31 \pm 0.19~ $\text{(stat.)}$ \pm 0.19~ $\text{(syst.)}$] \times 10^{-6}$and$ A_{CP} = +0.14 \pm 0.36~ $\text{(stat.)}$ \pm 0.10~ $\text{(syst.)}$, $ respectively. The signal significance, including the systematic uncertainty, is 6.4 standard deviations. We combine these results with Belle’s earlier measurements of $B^0\to {\pi }^{+}{\pi }^{-}$ and $B^{\pm }\to {\pi }^{\pm }{\pi }^0$ to exclude the $CP$-violating parameter ${\varphi }_2$ from the range $15.5^{\circ} < \phi_{2} < 75.0^{\circ}$ at 95% confidence level.