Realistic model for a fifth force explaining anomaly in ${}_{8}Be_{⁎}\to {}_{8}Be{e}^{+}{e}^{-}$ decay

We propose a theoretical model to explain a $6.8\sigma$ anomaly recently reported in the opening angle and invariant mass distributions of $e^{+}{e}^{-}$ pairs produced in excited ${}_{8}Be_{⁎}$ nuclear transition to its ground state ${}_{8}Be$. The anomaly is explained by a fifth force mediated by a 17 MeV X boson through the decay ${}_{8}Be_{⁎}\to {}_{8}BeX$ followed by $X\to e^{+}{e}^{-}$. The X boson comes from extension of the standard model with two additional U(1) gauge symmetries producing a protophobic pure vector current interaction with quarks. The model also contains axial-vector current interaction. Although the existent axial-vector current interactions are strongly constrained by the measurement of parity violation in e-quark scattering, their contributions cancel out in the iso-scalar interaction for ${}_{8}Be_{⁎}\to {}_{8}BeX$. It is remarkable that the model parameters need to explain the anomaly survive all known low energy experimental constraints. The model may also alleviate the long-standing ${(g-2)}_{\mu }$ anomaly problem and can be probed by the LHCb experiment.