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

We present a new measurement of the time-dependent CP-violating parameters in B{sup 0}{yields}{pi}{sup +}{pi}{sup -} decays with 275x10{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 666{+-}43 B{sup 0}{yields}{pi}{sup +}{pi}{sup -} events and measure the CP-violating parameters: S{sub {pi}}{sub {pi}}=-0.67{+-}0.16(stat){+-}0.06(syst) and A{sub {pi}}{sub {pi}}=+0.56{+-}0.12(stat){+-}0.06(syst). We find evidence for large direct CP violation with a significance greater than 4 standard deviations for any S{sub {pi}}{sub {pi}} value. Using isospin relations, we obtain 95.4% confidence intervals for the Cabibbo-Kobayashi-Maskawa quark-mixing matrix angle {phi}{sub 2} of 0 deg.