Observation of Direct $CP$ Violation in ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ Decays and Model-Independent Constraints on the Quark-Mixing Angle ${\ensuremath{\phi}}_{2}$

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Observation of Direct $C P$ Violation in $B^{0} \to π^{+} π^{-}$ Decays and Model-Independent Constraints on the Quark-Mixing Angle $ϕ_{2}$

H. Ishino et al. (The Belle Collaboration)

Phys. Rev. Lett. 98, 211801 – Published 21 May 2007

Abstract

We report a new measurement of the time-dependent $C P$ -violating parameters in $B^{0} \to π^{+} π^{-}$ decays with $535 \times 10^{6}$ $B \bar{B}$ pairs collected with the Belle detector at the KEKB asymmetric-energy $e^{+} e^{-}$ collider operating at the $Υ (4 S)$ resonance. We find $1464 \pm 65$ $B^{0} \to π^{+} π^{-}$ events and measure the $C P$ -violating parameters $S_{π π} = - 0.61 \pm 0.10 (stat) \pm 0.04 (syst)$ and $A_{π π} = + 0.55 \pm 0.08 (stat) \pm 0.05 (syst)$ . We observe large direct $C P$ violation with a significance greater than 5 standard deviations for any $S_{π π}$ value. Using isospin relations, we measure the Cabibbo-Kobayashi-Maskawa quark-mixing matrix angle $ϕ_{2} = (97 \pm 11) °$ for the solution consistent with the standard model and exclude the range $11 ° < ϕ_{2} < 79 °$ at the 95% confidence level.