Measurement of the branching fraction of $J/\psi \to \omega {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ and search for $J/\psi \to \omega X\left(1835\right)$, $X\left(1835\right)\to {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ decay

Using a sample of $1.31×{10}^{9}\text{}\text{}J/\psi $ events collected by the BESIII detector at BEPCII during 2009 and 2012, we study the $J/\psi \to \omega {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ hadronic process. For the first time, we measure the branching ratio $B\left(J/\psi \to \omega {\eta }^{\prime }{\pi }^{+}{\pi }^{-}\right)=\left(1.12±0.02±0.13\right)×{10}^{-3}$. We search for the $X\left(1835\right)$ state in the ${\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ invariant mass spectra. No evidence is found and we estimate the upper limit on the branching fraction at 90% confidence level to be $B\left(J/\psi \to \omega X\left(1835\right),X\left(1835\right)\to {\eta }^{\prime }{\pi }^{+}{\pi }^{-}\right)<6.2×{10}^{-5}$.