A Family-nonuniversal $U(1)^\prime$ Model for Excited Beryllium Decays

Excited beryllium has been observed to decay into electron-positron pairs with a $6.8~σ$ anomaly. The process is properly explained by a 17 MeV proto-phobic vector boson. In present work, we consider a family-nonuniversal $U(1)^{\prime}$ that is populated by a $U(1)^{\prime}$ gauge boson $Z^\prime$ and a scalar field $S$, charged under $U(1)^{\prime}$ and singlet under the Standard Model (SM) gauge symmetry. The SM chiral fermion and scalar fields are charged under $U(1)^{\prime}$ and we provide them to satisfy the anomaly-free conditions. The Cabibbo-Kobayashi-Maskawa (CKM) matrix is reproduced correctly by higher-dimension Yukawa interactions facilitated by $S$. The vector and axial-vector current couplings of the $Z^\prime$ boson to the first generation of fermions do satisfy all the bounds from the various experimental data. The $Z^\prime$ boson can have kinetic mixing with the hypercharge gauge boson and $S$ can directly couple to the SM-like Higgs field. The kinetic mixing of $Z^\prime$ with the hypercharge gauge boson, as we show by a detailed analysis, generates the observed beryllium anomaly. We find that beryllium anomaly can be properly explained by a MeV-scale sector with a minimal new field content. The minimal model we construct forms a framework in which various anomalous SM decays can be discussed.