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

A $6.8,sigma$ anomaly has been reported in the opening angle and invariant mass 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 can explain the data through the decay of an excited state to the ground state, ${^8Be^*} to {^8Be}, X$, and then the followed saturating decay $X to e^+e^-$. In this work we propose a renormalizable model to realize this fifth force. 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. Several other implications are discussed.