Improved measurement of ψ(3686)→ π⁺π⁻ η

Using a sample of (2712.4 ± 14.3) × 10⁶ $ψ(3686)$ events collected with the BESIII detector, we perform a partial wave analysis of the decay ψ(3686)→π⁺π⁻η with the π⁺π⁻ invariant mass in the ρ(770)⁰ mass region, [0.3, 2.2] GeV/c². The cross section line-shape around the $ψ(3686)$ resonance is measured using energy-scan data sets, enabling the estimation of continuum contribution and its interference with the $ψ(3686)$ resonance. The branching fraction of ψ(3686)→ρ(770)⁰η is determined to be (1.34 ± 0.03±0.13) × 10⁻⁵. The ψ(3686)→ a₂(1320)±π∓ decay is observed for the first time with a significance of $35.7σ$, and its partial branching fraction is measured to be (2.13 ± 0.05±0.32) × 10⁻⁵. The $η$-η^ pseudoscalar mixing angle θP is then found to be (-11.2 ± 1.6±3.6)^∘ or (-19.4± 3.1±5.7)^∘, where the first uncertainty is statistical and the second systematic.