We study the processes γγ → ηc → η0KþK−, η0πþπ−, and ηπþπ− using a data sample of 519 fb−1 recorded with the BABAR detector operating at the SLAC PEP-II asymmetric-energy e+e− collider at center-of-mass energies at and near the Υ(nS) (n = 2, 3, 4) resonances. This is the first observation of the decay ηc → η0KþK− and we measure the branching fraction Γðηc → η0KþK−Þ=ðΓðηc → η0πþπ−Þ 1⁄4 0.644 0.039stat 0.032sys. Significant interference is observed between γγ → ηc → ηπþπ− and the nonresonant two-photon process γγ → ηπþπ−. A Dalitz plot analysis is performed of ηc decays to η0KþK−, η0πþπ−, and ηπþπ−. Combined with our previous analysis of ηc → KK ̄ π, we measure the K 0ð1430Þ parameters and the ratio between its η0K and πK couplings. The decay ηc → η0πþπ− is dominated by the f0ð2100Þ resonance, also observed in J=ψ radiative decays. A new a0(1700)→ ηπ resonance is observed in the ηc → ηπþπ− channel. We also compare ηc decays to η and η0 final states in association with scalar mesons as they relate to the identification of the scalar glueball.
