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A $6.8\,\sigma$ anomaly has been reported in the opening angle and invariantmass distributions of $e^+e^-$ pairs produced in ${^8Be}$ nuclear transitions.It has been shown that a protophobic fifth force mediated by a$17\,\textrm{MeV}$ gauge boson $X$ with pure vector current interactions canexplain the data through the decay of an excited state to the ground state,${^8Be^*} \to {^8Be}\, X$, and then the followed saturating decay $X \toe^+e^-$. In this work we propose a renormalizable model to realize this fifthforce. Although axial-vector current interactions also exist in our model,their contributions cancel out in the iso-scalar interaction for ${^8Be^*} \to{^8Be} \,X$. Within the allowed parameter space, this model can alleviate the$(g-2)_\mu$ anomaly problem and can be probed by the LHCb experiment. Severalother implications are discussed.

Realistic model for a fifth force explaining anomaly in ${^8Be^*} \to {^8Be} \;{e^+e^-}$ Decay