Angles of the CKM Unitarity Triangle Measured at Belle

Abstract

The Belle experiment has used several methods to measure or constrain the angles phi_1, phi_2, and phi_3 (or beta, alpha, and gamma) of the CKM unitarity triangle. The results are sin(2phi_1) = 0.728 \pm 0.056 (stat) \pm 0.023 (syst) or phi_1= (23.4 +2.7 -2.4) degrees from B0 -> J/psi K0 decays (140 fb-1); phi_2 = 0-19 degrees or 71-180 degrees at 95.4% CL from B0 -> pi+pi- decays (253 fb-1); and phi_3 = [68 +14 -15 (stat) \pm 13 (syst) \pm 11 (model)] degrees from B+ -> (D0, D0bar) K+, (D0,D0bar) -> K0_S pi+ pi- decays (253 fb-1). These values satisfy the triangle relation phi_1 + phi_2 + phi_3 = 180 degrees within their uncertainties. The angle phi_1 is also determined from several b -> s qbar q penguin-dominated decay modes; the value obtained by taking a weighted average of the individual results differs from the B0 -> J/psi K0 result by more than two standard deviations. The angle phi_2 is constrained by measuring a CP asymmetry in the decay time distribution; the asymmetry observed is large, and the difference in the yields of B0,B0bar -> pi+ pi- decays constitutes the first evidence for direct CP violation in the B system.