Measurements of the branching fractions of the P-wave charmonium spin-singlet state hc(¹P₁) → h⁺ h⁻π⁰/η

Based on (2712.4± 14.3)×10⁶ ψ(3686) events, we investigate four hadronic decay modes of the P-wave charmonium spin-singlet state hc(¹P₁) → h⁺ h⁻ π⁰/η (h=π or K) via the process ψ(3686) → π⁰hc at BESIII. The hc → π⁺ π⁻ π⁰ decay is observed with a significance of 9.6σ after taking into account systematic uncertainties. Evidences for hc → K⁺ K⁻ π⁰ and hc → K⁺ K⁻ η are found with significances of 3.5σ and 3.3σ, respectively, after considering the systematic uncertainties. The branching fractions of these decays are measured to be B(hc → π⁺ π⁻ π⁰)=(1.36±0.16±0.14)×10⁻³, B(hc → K⁺ K⁻ π⁰)=(3.26±0.84±0.36)×10⁻⁴, and B(hc → K⁺ K⁻ η)=(3.13±1.08±0.38)×10⁻⁴, where the first uncertainties are statistical and the second are systematic. No significant signal of hc→π⁺π⁻η is found, and the upper limit of its decay branching fraction is determined to be B(hc→π⁺π⁻η) < 4.0 × 10⁻⁴ at 90% confidence level.