Partial wave analyses of $ \psi (3686)\to p\overline{p}{\pi }^{0}$ and $ \psi (3686)\to p\overline{p}\eta $

Using a sample of $ (2712\pm 14)\times {10}^{6}\text{}\text{}\psi (3686)$ events collected with the BESIII detector, we perform partial wave analyses of the decays $ \psi (3686)\to p\overline{p}{\pi }^{0}$ and $ \psi (3686)\to p\overline{p}\eta $. The branching fractions of $ \psi (3686)\to p\overline{p}{\pi }^{0}$ and $ \psi (3686)\to p\overline{p}\eta $ are determined to be $ (133.9\pm 11.2\pm 2.3)\times {10}^{-6}$ or $ (183.7\pm 13.7\pm 3.2)\times {10}^{-6}$ and $ (61.5\pm 6.5\pm 1.1)\times {10}^{-6}$ or $ (84.4\pm 6.9\pm 1.4)\times {10}^{-6}$, respectively, where the two solutions are caused by an ambiguous phase angle between resonant and continuum processes. Several well-established $ {N}^{*}$ states are observed in the $ p{\pi }^{0}$ and $ p\eta $ systems, and the corresponding branching fractions are measured. The ratio of decay widths $ {\mathrm{\Gamma }}_{N(1535)\to N\eta }/{\mathrm{\Gamma }}_{N(1535)\to N\pi }$ is determined to be $ 0.99\pm 0.05\pm 0.19$.