Observation of Direct CP Violation in B{sup 0}{yields}{pi}{sup +}{pi}{sup -} Decays and Model-Independent Constraints on the Quark-Mixing Angle {phi}{sub 2}

We report a new measurement of the time-dependent CP-violating parameters in B{sup 0}{yields}{pi}{sup +}{pi}{sup -} decays with 535x10{sup 6} BB pairs collected with the Belle detector at the KEKB asymmetric-energy e{sup +}e{sup -} collider operating at the {upsilon}(4S) resonance. We find 1464{+-}65 B{sup 0}{yields}{pi}{sup +}{pi}{sup -} events and measure the CP-violating parameters S{sub {pi}}{sub {pi}}=-0.61{+-}0.10(stat){+-}0.04(syst) and A{sub {pi}}{sub {pi}}=+0.55{+-}0.08(stat){+-}0.05(syst). We observe large direct CP violation with a significance greater than 5 standard deviations for any S{sub {pi}}{sub {pi}} value. Using isospin relations, we measure the Cabibbo-Kobayashi-Maskawa quark-mixing matrix angle {phi}{sub 2}=(97{+-}11) deg. for the solution consistent with the standard model and exclude the range 11 deg.