Search for CP violation in D(s)⁺ → h⁺ π⁰ and decays D(s)⁺ → h⁺ η decays

Searches for CP violation in the two-body decays D-(s)(+) -> h(+)pi(0) and D-(s)(+) -> h(+)eta (where h(+) denotes a pi(+) or K+ meson) are performed using pp collision data collected by the LHCb experiment corresponding to either 9 fb(-1) or 6 fb(-1) of integrated luminosity. The pi(0) and eta mesons are reconstructed using the e(+) e(-)gamma final state, which can proceed as three-body decays pi(0) -> e(+) e(-) gamma and eta -> e(+) e(-)gamma, or via the two-body decays pi(0) -> gamma gamma and eta -> gamma gamma followed by a photon conversion. The measurements are made relative to the control modes D-(s)(+) K(S)(0)h(+) to cancel the production and detection asymmetries. The CP asymmetries are measured to be A(CP)(D+ -> pi(+)pi(0)) = (-1.3 +/- 0.9 +/- 0.6)%, A(CP)(D+ -> K+pi(0)) = (- 3.2 +/- 4.7 +/- 2.1)%, A(CP)(D+ -> pi(+)eta) = (-0.2 +/- 0.8 +/- 0.4)%, A(CP)(D+ -> K+eta) = (-6 +/- 10 +/- 4 )%, A(CP)(D-s(+) -> K+pi(0)) = (-0.8 +/- 3.9 +/- 1.2)%, A(CP)(D-s(+) -> pi(+)eta) = ( 0.8 +/- 0.7 +/- 0.5)%, A(CP)(D-s(+) -> K+eta) = ( 0.9 +/- 3.7 +/- 1.1)%, where the first uncertainties are statistical and the second systematic. These results are consistent with no CP violation and mostly constitute the most precise measurements of A(CP) in these decay modes to date.