Measurements of the branching fractions of the P-wave charmonium spin-singlet state hc (¹P₁) h^+ h^-⁰/

Based on (2712. 4 14. 3) 10^6 (3686) events, we investigate four hadronic decay modes of the P-wave charmonium spin-singlet state hc (¹P₁) h^+ h^- ⁰/ (h= or K) via the process (3686) ^0hc at BESIII. The hc ^+ ^- ⁰ decay is observed with a significance of 9. 6 after taking into account systematic uncertainties. Evidences for hc K^+ K^- ⁰ and hc K^+ K^- are found with significances of 3. 5 and 3. 3, respectively, after considering the systematic uncertainties. The branching fractions of these decays are measured to be B (hc ^+ ^- ⁰) = (1. 360. 160. 14) 10^-3, B (hc K^+ K^- ⁰) = (3. 260. 840. 36) 10^-4, and B (hc K^+ K^-) = (3. 131. 080. 38) 10^-4, where the first uncertainties are statistical and the second are systematic. No significant signal of hc^+^- is found, and the upper limit of its decay branching fraction is determined to be B (hc^+^-) < 4. 0 10^-4 at 90% confidence level.