Is there a sign of new physics in beryllium transitions?

A 6.8$\sigma$ anomaly in the invariant mass distribution of $e^+ e^-$ pairs produced via internal pair creation in $^8{\rm Be}$ nuclear transitions has been reported recently by Krasznahorkay et al.$~$in Phys.$~$Rev.$~$Lett.$~$116 (2016) 042501. The data can be explained by a $\sim\,$17 MeV vector gauge boson $X$ produced in the transition of an excited beryllium state to the ground state, $^8{\rm Be}^* \rightarrow \, ^8{\rm Be} \, X$, followed by the decay $X \rightarrow e^+ e^-$. We find that the gauge boson $X$ can be associated with a new ``protophobic'' fifth force (i.e.$~$with a coupling to protons suppressed compared to its coupling to neutrons) with a characteristic range of $\sim\,$10 fm and milli-charged couplings to first generation quarks and electrons. We show that such a ``protophobic'' gauge boson is consistent with all available experimental constraints and we discuss several ways to embed this new particle into an anomaly-free extension of the Standard Model. One of the most appealing theories of this type is a model with gauged baryon number, in which the new gauge boson kinetically mixes with the photon, and provides a portal to the dark matter sector. Apart from the phenomenological richness of the model, it can also alleviate the current 3.6$\sigma$ discrepancy between the predicted and measured values of the muon's anomalous magnetic moment.