Interpretation of the 17 MeV anomaly in $^8$Be$^*$ decay as light, weakly coupled new physics*

Recently a 6.8$\sigma$ anomaly has been reported in the opening angle and invariant mass distributions of $e^+ e^-$ pairs produced in $^8$Be nuclear transitions (Krasznahorkay et al., PRL 116 (2016) 042501). We find that the data can be explained by a 17 MeV vector gauge boson $X$ that is produced in the decay ${}^8{\rm Be}^* \to {}^8{\rm Be}\, X$, with $X$ decaying through $X \to e^+ e^-$. The $X$ boson mediates a new force with a characteristic range of 12 fm, and it has milli-charged couplings to up and down quarks and electrons, yielding a proton coupling that is suppressed relative to neutrons. We show that such a "protophobic" $X$ boson is compatible with all other experimental constraints in this mass range and discuss how such an object can emerge from fundamental physics. The $X$ boson may also alleviate the current 3.6$\sigma$ discrepancy between the predicted and measured values of the muon's anomalous magnetic moment.