Sensitivity of the ${\eta }^{(\mathrm{\prime })}\to {\pi }^0\gamma \gamma$ and ${\eta }^{\mathrm{\prime }}\to \eta \gamma \gamma$ decays to a sub-GeV leptophobic $U(1{)}_B$ boson

The sensitivity of the rare decays ${\eta }^{(\mathrm{\prime })}\to {\pi }^0\gamma \gamma$ and ${\eta }^{\mathrm{\prime }}\to \eta \gamma \gamma$ to signatures of a leptophobic $B$ boson in the MeV-GeV mass range is analyzed in this work. By adding an explicit $B$-boson resonance exchange, $\eta \to B\gamma \to {\pi }^0\gamma \gamma$, to the Standard Model contributions from vector and scalar meson exchanges, and employing experimental data for the associated branching ratios, it allows us to improve the current constraints on the $B$-boson mass $m_B$ and coupling to Standard Model particles ${\alpha }_B$. From these constraints and the analysis of the available experimental $\gamma \gamma$ invariant mass distribution, we show that a $B$-boson signature in the resonant mass range $m_{{\pi }^0}\lesssim m_B\lesssim m_{\eta }$ is strongly suppressed and would be very difficult to experimentally identify, assuming that the leptophobic $B$ boson only decays to Standard Model particles. In contrast, the limits outside this mass window are less stringent and the corresponding $t$- and $u$-channel signatures may still be observable in the data, as it occurs with the nonresonant Standard Model $\rho$, $\omega$ and $\phi$ meson exchanges. In addition, we make use of experimental data from the ${\eta }^{\mathrm{\prime }}\to {\pi }^0\gamma \gamma$ and ${\eta }^{\mathrm{\prime }}\to \eta \gamma \gamma$ decays to explore larger $B$-boson masses. Our results are relevant for the $B$-boson search programs at existing and forthcoming light-meson facilities, such as KLOE(-II) and Jefferson Lab Eta Factory experiments.