Improved Evidence for Direct $C P$ Violation in $B^{0} \to π^{+} π^{-}$ Decays and Model-Independent Constraints on $ϕ_{2}$

We present a new measurement of the time-dependent

C P

-violating parameters in

B^{0} \to π^{+} π^{-}

decays with

275 \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

666 \pm 43

B^{0} \to π^{+} π^{-}

events and measure the

C P

-violating parameters:

S_{π π} = - 0.67 \pm 0.16 (stat) \pm 0.06 (syst)

and

A_{π π} = + 0.56 \pm 0.12 (stat) \pm 0.06 (syst)

. We find evidence for large direct

C P

violation with a significance greater than 4 standard deviations for any

S_{π π}

value. Using isospin relations, we obtain 95.4% confidence intervals for the Cabibbo-Kobayashi-Maskawa quark-mixing matrix angle

ϕ_{2}

0 ° < ϕ_{2} < 19 °

and

71 ° < ϕ_{2} < 180 °

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Improved Evidence for DirectCPViolation inB0→π+π−Decays and Model-Independent Constraints onϕ2