Observation of DirectCPViolation inB0→π+π−Decays and Model-Independent Constraints on the Quark-Mixing Angleϕ2

We report a new measurement of the time-dependent $CP$-violating parameters in $B^0\to {\pi }^{+}{\pi }^{-}$ decays with $535\times {10}^6$ $B\overline{B}$ pairs collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider operating at the ${\rm Y}(4S)$ resonance. We find $1464\pm 65$ $B^0\to {\pi }^{+}{\pi }^{-}$ events and measure the $CP$-violating parameters ${\mathcal{S}}_{\pi \pi }=-0.61\pm 0.10(\mathrm{stat})\pm 0.04(\mathrm{syst})$ and ${\mathcal{A}}_{\pi \pi }=+0.55\pm 0.08(\mathrm{stat})\pm 0.05(\mathrm{syst})$. We observe large direct $CP$ violation with a significance greater than 5 standard deviations for any ${\mathcal{S}}_{\pi \pi }$ value. Using isospin relations, we measure the Cabibbo-Kobayashi-Maskawa quark-mixing matrix angle ${\varphi }_2=(97\pm 11)°$ for the solution consistent with the standard model and exclude the range $11°<{\varphi }_2<79°$ at the 95% confidence level.