Particle physics models for the 17 MeV anomaly in beryllium nuclear decays

The $6.8\ensuremath{\sigma}$ anomaly in excited $^{8}\mathrm{Be}$ nuclear decays via internal pair creation is fit well by a new particle interpretation. In a previous analysis, we showed that a 17 MeV protophobic gauge boson provides a particle physics explanation of the anomaly consistent with all existing constraints. Here we begin with a review of the physics of internal pair creation in $^{8}\mathrm{Be}$ decays and the characteristics of the observed anomaly. To develop its particle interpretation, we provide an effective operator analysis for excited $^{8}\mathrm{Be}$ decays to particles with a variety of spins and parities and show that these considerations exclude simple models with scalar particles. We discuss the required couplings for a gauge boson to give the observed signal, highlighting the significant dependence on the precise mass of the boson and isospin mixing and breaking effects. We present anomaly-free extensions of the Standard Model that contain protophobic gauge bosons with the desired couplings to explain the $^{8}\mathrm{Be}$ anomaly. In the first model, the new force carrier is a ${\mathrm{U}(1)}_{B}$ gauge boson that kinetically mixes with the photon; in the second model, it is a $\mathrm{U}(1{)}_{B\ensuremath{-}L}$ gauge boson with a similar kinetic mixing. In both cases, the models predict relatively large charged lepton couplings $\ensuremath{\sim}0.001$ that can resolve the discrepancy in the muon anomalous magnetic moment and are amenable to many experimental probes. The models also contain vectorlike leptons at the weak scale that may be accessible to near future LHC searches.