Sensitivity of the $η^{(\prime)}\toπ^{0}γγ$ and $η^{\prime}\toηγγ$ decays to a sub-GeV leptophobic $U(1)_{B}$ boson

Abstract

The sensitivity of the rare decays $η^{(\prime)}\toπ^{0}γγ$ and $η^{\prime}\toηγγ$ 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, $η\to Bγ\toπ^{0}γγ$, 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 $α_{B}$. From these constraints and the analysis of the available experimental $γγ$ invariant mass distribution, we show that a $B$-boson signature in the resonant mass range $m_{π^{0}}\lesssim m_{B}\lesssim m_η$ 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 $ρ$, $ω$ and $ϕ$ meson exchanges. In addition, we make use of experimental data from the $η^{\prime}\toπ^{0}γγ$ and $η^{\prime}\toηγγ$ 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.