Production-Dependent Interpretation of the KLOE--MAMI $η\!\to\!π^{0}γγ$ Tension via the Nucleon-Triggered Leptophobic Vector $V_{\!\mathcal B}$

TL;DR

This paper confronts a notable discrepancy between KLOE's leptonic η→π^0 γγ measurement and the MAMI-based, nucleon-induced rate, proposing a production-dependent New Physics scenario with a nucleon-triggered vector V_B in the 1.5–5 GeV range. The authors build a UV-complete framework involving a scalaron S and a dark pion π_D that generate an effective nucleon-current operator coupling to P and V_B, encapsulated by a single universal coefficient C_eff fit to MAMI data. They predict measurable enhancements in related η′ decays under nucleon production (roughly ~10% in η′→π^0 γγ) and an A^2 scaling with nuclear targets, while keeping purely leptonic channels SM-like, enabling decisive falsification via dedicated photoproduction and nuclear-target experiments. The work outlines a coherent experimental program—comparing nucleon-triggered and leptonic production, direct photoproduction searches, and heavy-nucleus studies—to confirm or exclude the nucleon-rescaled, leptophobic-vector interpretation of the KLOE–MAMI tension.

Abstract

The recent KLOE measurement $\mathrm{BR}^{η\rightarrowπ^{0}γγ}_{\text{KLOE}} = (0.98\pm0.11_{\text{stat}}\pm0.14_{\text{syst}})\times10^{-4}$ is less than half the current world average, $(2.55\pm0.22)\times10^{-4}$, dominated by MAMI photoproduction data. We show that this $\approx 5.5\, σ$ 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 \(\bigl(\bar N N\bigr)\,\widetilde V_{\mathcal{B}}^{μν}F_{μν}P\). This interaction modifies the \(η^{(\prime)}\!\to\!π^{0}\left(η\right)γγ\) decay rates \textit{only} in the processes involving an external nucleon current, \(γp\!\to\!η^{(\prime)}p\) and \(π^-p\!\to\!η^{(\prime)}n\), but leaves purely leptonic production channels, such as \(e^+e^-\to φ\toη^{(\prime)}γ\) at KLOE and \(e^+e^-\to J/ψ\toγη^{(\prime)}\) at BESIII, Standard-Model-like. The same mechanism predicts a \(\approx 10\%\) nucleon-triggered enhancement of the \(η^\prime\!\to\!π^{0}γγ\) decay rate and a negligible shift for \(η^\prime\!\to\!ηγγ\), 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, $γp\!\to\!V_{\!\mathcal B}\,π^{0} p$. An integrated experimental program that compares $η^{(\prime)}\!\to\!π^{0}(η)γγ$ 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.

Figures (6)

• Figure 1: The dominant VMD diagrams contributing to the $\eta^{\left(\prime\right)}\rightarrow\pi^0\left(\eta\right)\gamma\gamma$ decays, corresponding to Eqn. \ref{['VMD']}.
• Figure 2: Photoproduction of the dark vector $V_{\!\mathcal{B}}$ on a nucleon target, $\gamma\,+\,N\!\to\!V_{\!\mathcal{B}}\,+\, P\,+\, N$, with the subsequent decay $V_{\!\mathcal{B}}\!\to\!\pi_D\gamma$, if kinematically allowed.
• Figure 3: Dominant Standard Model and nucleon-triggered New Physics contributions to $\eta^{(\prime)}\!\rightarrow\!\pi^{0}(\eta)\gamma\gamma$ decays. In the Standard Model (left two diagrams), the nucleon acts as a spectator, and the decay proceeds via vector-meson dominance through intermediate $V\!\in\!\{\omega,\rho^{0},\phi\}$. In the New Physics sector (right two diagrams), the nucleon triggers the scalar portal $S$, which links the visible pseudoscalar $P$ to dark pions $\pi_{D}$ and to the isoscalar dark vector $V_{\!\mathcal{B}}$, generating an additional $V_{\!\mathcal{B}}P\gamma$ amplitude.
• Figure 4: Differential $\gamma\gamma$ spectrum in subfigure (a) and $\pi^{0}\gamma$ spectrum in subfigure (b) for the $\eta\!\to\!\pi^{0}\gamma\gamma$ decay. In both panels, the dashed green curve shows the Standard Model prediction, while the solid blue curve represents the nucleon-triggered scenario including $V_{\!\mathcal{B}}$. The new interaction induces an almost uniform upward shift across the spectra.
• Figure 5: Differential $\gamma\gamma$ spectrum in subfigure (a) and $\pi^{0}\gamma$ spectrum in subfigure (b) for the $\eta^\prime\!\to\!\pi^{0}\gamma\gamma$ decay. The $V_\mathcal{B}$ term produces a $\sim 10\%$ increase in the nucleon-triggered production environment (blue versus green), smaller than in the $\eta$ case, since the $\omega$ meson is on shell and dominates the overall Standard Model amplitude.