Evidence for direct CP violation in B±â†’ηh± and observation of B0→ηK0.

We report measurements of the branching fractions and CP asymmetries for B(±)→ηh(±) (h=K or π) and the observation of the decay B(0)→ηK(0) from the final data sample of 772×10(6) B ̅B pairs collected with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. The measured branching fractions are B(B(±)→ηK(±))=(2.12±0.23±0.11)×10(-6), B(B(±)→ηπ(±))=(4.07±0.26±0.21)×10(-6), and B(B(0)→ηK(0))=(1.27(-0.29)(+0.33)±0.08)×10(-6), where the last decay is observed for the first time with a significance of 5.4 standard deviations (σ). We also find evidence for CP violation in the charged B modes, A(CP)(B(±)→ηK(±))=-0.38±0.11±0.01 and A(CP)(B(±)→ηπ(±))=-0.19±0.06±0.01 with significances of 3.8 σ and 3.0 σ, respectively. For all measurements, the first and second uncertainties are statistical and systematic, respectively.