Improved measurement of the branching fraction of h_c → γη′/η and search for h_c→ γπ⁰

The processes h_c→ γP (P = η′, η, π⁰) are studied with a sample of (27.12 ± 0.14) × 10⁸ψ(3686) events collected by the BESIII detector at the BEPCII collider. The decay h_c→ 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 (h_c→ 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) → π⁰h_c. The combination of these results allows for a precise determination of Rh_c=Bh_c→γηBh_c→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 h_c → γπ⁰, and an upper limit is placed on its branching fraction of B(h_c → γπ⁰) < 5.0 × 10⁻⁵, at the 90% confidence level.