We present an improved measurement of $\mathrm{CP}$-violating asymmetries in $B^0\to {\pi }^{+}{\pi }^{-}$ decays based on a $78{\mathrm{fb}}^{-1}$ data sample collected at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We reconstruct one neutral B meson as a $B^0\to {\pi }^{+}{\pi }^{-}$ $\mathrm{CP}$ eigenstate and identify the flavor of the accompanying B meson from inclusive properties of its decay products. We apply an unbinned maximum likelihood fit to the distribution of the time intervals between the two B meson decay points. The fit yields the $\mathrm{CP}$-violating asymmetry amplitudes ${\mathcal{A}}_{\pi \pi }=+0.77\mathrm{}\pm 0.27\left(\mathrm{stat}\right)\pm 0.08\left(\mathrm{syst}\right)$ and ${\mathcal{S}}_{\pi \pi }=-1.23\pm 0.41\left(\mathrm{stat}\right){}_{-0.07}^{+0.08\mathrm{}}\left(\mathrm{syst}\right),$ where the statistical uncertainties are determined from the Monte Carlo pseudoexperiments. We obtain confidence intervals for $\mathrm{CP}$-violating asymmetry parameters ${\mathcal{A}}_{\pi \pi }$ and ${\mathcal{S}}_{\pi \pi }$ based on a frequentist approach. We rule out the $\mathrm{CP}$-conserving case, ${\mathcal{A}}_{\pi \pi }={\mathcal{S}}_{\pi \pi }=0,$ at the $99.93\%$ confidence level. We discuss how these results constrain the value of the Cabibbo-Kobayashi-Maskawa (CKM) angle ${\phi }_2.$

• Received 23 January 2003

DOI:https://doi.org/10.1103/PhysRevD.68.012001