Measurement of the branching fraction for the decay $ {\chi }_{cJ}\to p\overline{p}\eta {\pi }^{0}$

Using $ (2712.4\pm 14.3)\times {10}^{6}\psi (3686)$ events collected by the BESIII detector operating at the BEPCII collider, we present the first observations of the decays $ {\chi }_{cJ}(J=0,1,2)\to p\overline{p}\eta {\pi }^{0}$. Their decay branching fractions are determined to be $ \mathcal{B}({\chi }_{c0}\to p\overline{p}\eta {\pi }^{0})=(2.42\pm 0.07\pm 0.19)\times {10}^{-4}$, $ \mathcal{B}({\chi }_{c1}\to p\overline{p}\eta {\pi }^{0})=\phantom{\rule{0ex}{0ex}}(1.95\pm 0.05\pm 0.12)\times {10}^{-4}$, and $ \mathcal{B}({\chi }_{c2}\to p\overline{p}\eta {\pi }^{0})=(1.33\pm 0.05\pm 0.08)\times {10}^{-4}$, where the first uncertainties are statistical and the second systematic.