Observation of D+ -> K+eta(()'()) and Search for CP Violation in D+ -> pi(+)eta(()'()) Decays

We report the first observation of the doubly Cabibbo-suppressed decays D+ -> K+eta(()'()) using a 791 fb(-1) data sample collected with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. The ratio of the branching fractions of doubly Cabibbo-suppressed relative to singly Cabibbo-suppressed D+ -> pi(+)eta(()'()) decays are B(D+ -> K+eta) / B(D+ -> pi(+)eta) =(3.06 +/- 0.43 +/- 0.14)% and B(D+ -> K+eta')/B(D+->pi(+)eta') = (3.77 +/- 0.39 +/- 0.10)%. From these, we find that the relative final-state phase difference between the tree and annihilation amplitudes in D+ decays, delta(TA), is (72 +/- 9)degrees or (288 +/- 9)degrees. We also report the most precise measurements of CP asymmetries to date: A(CP)(D+->pi+eta) = (+1.74 +/- 1.13 +/- 0.19)% and A(CP)(D+->pi+eta') = (-0.12 +/- 1.12 +/- 0.17)%.