Search for new hadronic decays of $h_{c}$ and observation of $h_{c}\to p\bar{p}η$

A search for the hadronic decays of the $h_{c}$ meson to the final states $p\bar{p}π^{+}π^{-}π^{0}$, $p\bar{p}η$, and $p\bar{p}π^0$ via the process $ψ(3686) \to π^{0}{h_c}$ is performed using $(4.48\pm0.03)\times10^{8}$ $ψ(3686)$ events collected with the BESIII detector. The decay channel $h_{c}\to p\bar{p}η$ is observed for the first time with a significance greater than $5σ$ and a branching fraction of $\left( {6.41 \pm 1.74 \pm 0.53 \pm 1.00} \right) \times {10^{ -4}}$, where the uncertainties are statistical, systematic, and that from the branching fraction of $ψ(3686)\toπ^{0}h_{c}$. Strong evidence for the decay ${h_c} \to p\bar{p}{π^+}{π^-}{π^0}$ is found with a significance of $4.9σ$ and a branching fraction of $\left( {3.84 \pm 0.83 \pm0.69} \pm 0.58 \right) \times {10^{ - 3}}$. The significances include systematic uncertainties. No clear signal of the decay $h_c\to p\bar{p}π^{0}$ is found, and an upper limit of $6.59\times 10^{-4}$ on its branching fraction is set at the 90% confidence level.