Improved measurement of the branching fraction of hc→γη^/η and search for hc→γπ⁰

The processes hc→γ P(P = η^,~η,~π⁰) are studied with a sample of (27.12±0.14)×10⁸ ψ(3686) events collected by the BESIII detector at the BEPCII collider. The decay hc→γη is observed for the first time with the significance of 9.0\,σ, and the branching fraction is determined to be (3.77±0.55±0.13±0.26)×10⁻⁴, while B(hc→γη⁾ is measured to be (1.40±0.11±0.04±0.10)×10⁻³, where the first uncertainties are statistical, the second systematic, and the third from the branching fraction of ψ(3686)→π⁰hc. The combination of these results allows for a precise determination of Rhc=B(hc→γη)/B(hc→γη⁾, which is calculated to be (27.0±4.4±1.0)%. The results are valuable for gaining a deeper understanding of η-η^ mixing, and its manifestation within quantum chromodynamics. No significant signal is found for the decay hc→γπ⁰, and an upper limit is placed on its branching fraction of B(hc→γπ⁰)<5.0×10⁻⁵, at the 90$%$ confidence level.