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In this work, we study the role of triangle singularity in the $J/\psi \to\gamma \bar{p} \Delta$ decay. We find that through a triangle mechanism,involving a triangle loop composed by $\omega$, $\pi$ and $p$, this decay maydevelop a triangle singularity and produce a visible peak in the invariant mass$M_{\gamma\Delta}$ around 1.73 GeV with a width of 0.02 GeV. Such a trianglemechanism may also cause significant spin effects on the final $\Delta$, whichcan be detected by measuring its spin density matrix elements. Our calculationsshow that the branching ratios due to the triangle mechanism is Br($J/\psi\to\gamma \bar p\Delta,\Delta\to \pi p$)=$1.058\times 10^{-6}$. Hopefully, thisreaction can be investigated at BESIII and future experiments, e.g. SuperTau-Charm Facility, and the narrow width of the induced structure, the movingTS position and the distinct features of the spin density matrix elements ofthe $\Delta$ may serve as signals for the triangle singularity mechanism.

Triangle singularity in the $J/\psi \to \gamma \bar{p} \Delta$ decay