Kinematic Fingerprints of a Nucleon-Triggered $V_{\mathcal{B}}$ in Rare $η^{(\prime)}\toπ^0(η)γγ$ Decays on Nucleon Targets

The nucleon-triggered vector boson $V_{\mathcal B}$ is a hypothetical particle motivated by a statistically significant discrepancy between the KLOE measurement, $\mathrm{BR}^{η\rightarrowπ^{0}γγ}_{\text{KLOE}} = \left(0.98\pm0.11_{\text{stat}}\pm0.14_{\text{syst}}\right)\times10^{-4}$, and the curr