Production-Dependent Interpretation of the KLOE--MAMI $\eta \to {\pi }^0\gamma \gamma$ Tension via the Nucleon-Triggered Leptophobic Vector $V_{\mathcal{B}}$

Abstract

The recent KLOE measurement ${\mathrm{BR}}_{\text{KLOE}}^{\eta \to {\pi }^0\gamma \gamma }=(0.98\pm 0.11_{\text{stat}}\pm 0.14_{\text{syst}})\times 10^{-4}$ is less than half the current world average, $(2.55\pm 0.22)\times 10^{-4}$, dominated by MAMI photoproduction data. We show that this $\approx 5.5\sigma$ discrepancy can be resolved by the new leptophobic, nucleon-triggered vector particle $V_{\mathcal{B}}$ with \(1.5~\text{GeV}\lesssim m_{V_{\!\mathcal B}}\lesssim5~\text{GeV}\), coupled via the effective operator \(\bigl(\bar N N\bigr)\,\widetilde V_{\mathcal{B}}^{\mu\nu}F_{\mu\nu}P\). This interaction modifies the \(\eta^{(\prime)}\!\to\!\pi^{0}\left(\eta\right)\gamma\gamma\) decay rates \textit{only} in the processes involving an external nucleon current, \(\gamma p\!\to\!\eta^{(\prime)}p\) and \(\pi^-p\!\to\!\eta^{(\prime)}n\), but leaves purely leptonic production channels, such as \(e^+e^-\to \phi\to\eta^{(\prime)}\gamma\) at KLOE and \(e^+e^-\to J/\psi\to\gamma\eta^{(\prime)}\) at BESIII, Standard-Model-like. The same mechanism predicts a \(\approx 10\%\) nucleon-triggered enhancement of the \(\eta^\prime\!\to\!\pi^{0}\gamma\gamma\) decay rate and a negligible shift for \(\eta^\prime\!\to\!\eta\gamma\gamma\), together with an \(\rm{A}^{2}\)-scaling boost if produced on heavy nuclei instead of protons. $V_{\mathcal{B}}$ can be searched directly in $2\to 3$ photoproduction, for example, $\gamma p\to V_{\mathcal{B}}{\pi }^{0}p$. An integrated experimental program that compares ${\eta }^{(\prime )}\to {\pi }^0(\eta )\gamma \gamma$ in the presence of external nucleon currents with purely leptonic production, and conducts direct photoproduction searches for a GeV-scale vector, can decisively confirm or exclude our nucleon-rescaled, leptophobic-vector interpretation of the KLOE--MAMI discrepancy.