The decay $J/psi rightarrow omega p bar{p}$ has been studied, using $225.3times 10^{6}$ $J/psi$ events accumulated at BESIII. No significant enhancement near the $pbar{p}$ invariant-mass threshold (denoted as $X(pbar{p})$) is observed. The upper limit of the branching fraction $mathcal{B}(J/psi rightarrow omega X(pbar{p}) rightarrow omega p bar{p})$ is determined to be $3.9times10^{-6}$ at the 95% confidence level. The branching fraction of $J/psi rightarrow omega p bar{p}$ is measured to be $mathcal{B}(J/psi rightarrow omega p bar{p}) =(9.0 pm 0.2 (text{stat.})pm 0.9 (text{syst.})) times 10^{-4}$.
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