We report the first observation of $CP$ violation in $B^0\to {\pi }^{+}{\pi }^{-}$ decays based on $152\times {10}^6$ $\Upsilon \left(4S\right)\to B\overline{B}$ decays collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We reconstruct a $B^0\to {\pi }^{+}{\pi }^{-}$ $CP$ eigenstate and identify the flavor of the accompanying $B$ meson from its decay products. From the distribution of the time intervals between the two $B$ meson decay points, we obtain ${\mathcal{A}}_{\pi \pi }=+0.58\pm 0.15\left(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\right)\pm 0.07\left(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\right)$ and ${\mathcal{S}}_{\pi \pi }=-1.00\pm 0.21\left(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\right)\pm 0.07\left(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\right)$. We rule out the $CP$-conserving case, ${\mathcal{A}}_{\pi \pi }={\mathcal{S}}_{\pi \pi }=0$, at a level of 5.2 standard deviations. We also find evidence for direct $CP$ violation with a significance at or greater than 3.2 standard deviations for any ${\mathcal{S}}_{\pi \pi }$ value.

• Received 18 January 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.021601