Observation of D⁺→K⁺η(′ and search for CP violation in D⁺→π⁺η(′) decays

We report the first observation of the doubly Cabibbo-suppressed decays D⁺→K⁺η(′) using a 791fb^-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 ⁺→π⁺η(′) decays are B(D ⁺→K⁺η)/B(D⁺→π⁺η )=(3.06±0.43±0.14)% and B(D⁺→K⁺η ^′)/B(D⁺→π⁺η ^′)=(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, δ_TA, is (72±9)°or (288±9)°. We also report the most precise measurements of CP asymmetries to date: ACPD⁺→π ⁺η=(+1.74±1.13±0.19)% and ACPD⁺→ π⁺η^′=(-0.12±1.12±0.17)%.