First Evidence for an Unambiguous Triangle Singularity from $\psi(2S) \to p\bar{p}\eta$
Triangle singularities, predicted by Landau in 1959, are purely kinematic enhancements arising from hadronic rescattering loops. Despite their proposed role in various anomalous decay processes and exotic hadron candidates, a direct experimental confirmation has remained elusive for more than six decades. We analyze the $p\eta/\bar{p}\eta$ invariant mass spectrum in $\psi(2S) \to p\bar{p}\eta$ measured by the BESIII Collaboration. The data exhibit a clear cusp-like structure around 1.564~GeV in the $N(1535)$ region, in precise agreement with the kinematic position predicted for the triangle singularity. Including the triangle singularity loop in the fit substantially improves the description of the data, with $\chi^2/\mathrm{d.o.f.}$ decreasing from 1.22 to 0.90, corresponding to a significance of $\sim 3.8\sigma$ for the triangle singularity contribution. The precise alignment of the observed excess with the predicted kinematic position provides the first compelling evidence for the triangle singularity effect.