We report a study of Lambda(+)(c)-> Lambda h(+) and Lambda(+)(c)-> Sigma(0)h(+) (h = K, pi) decays based on a data sample of 980 fb(-1) collected with the Belle detector at the KEKB energy-asymmetric e(+)e(-) collider. The first results of direct CP asymmetry in two-body singly Cabibbo-suppressed (SCS) decays of charmed baryons are measured, A(CP)(dir)(Lambda(+)(c)-> Lambda K+) = +0.021 +/- 0.026 +/- 0.001 and A(CP)(dir)(Lambda(+)(c)-> Sigma K-0(+)) = +0.025 +/- 0.054 +/- 0.004.
We also make the most precise measurement of the decay asymmetry parameters (alpha) for the four modes of interest and search for CP violation via the alpha-induced CP asymmetry (A(CP)(alpha)). We measure A(CP)(alpha)(Lambda(+)(c)-> Lambda K+) = -0.023 +/- 0.086 +/- 0.071 and A(CP)(alpha)(Lambda(+)(c)-> Sigma K-0(+)) = +0.08 +/- 0.35 +/- 0.14, which are the first A(CP)(alpha) results for SCS decays of charmed baryons.
We search for Lambda-hyperon CP violation in Lambda(+)(c)-> Lambda(+)(c)-> (Lambda, Sigma(0))pi(+) and find A(CP)(alpha)(Lambda -> p pi(-)) = +0.013 +/- 0.007 +/- 0.011. This is the first time that hyperon CP violation has been measured via Cabibbo-favored charm decays.
No evidence of baryon CP violation is found. We also obtain the most precise branching fractions for two SCS Lambda(c+) decays, B(Lambda(+)(c) -> Lambda K+) = (6.57 +/- 0.17 +/- 0.11 +/- 0.35) x 10(-4) and B(Lambda(+)(c) -> Sigma K-0(+)) = (3.58 +/- 0.19 +/- 0.06 +/- 0.19) x 10(-4).
The first uncertainties are statistical and the second systematic, while the third uncertainties come from the uncertainties on the world average branching fractions of Lambda(+)(c)-> (Lambda, Sigma(0))pi(+).