Atomki Anomaly in Family-Dependent $U(1{)}^{\prime }$ Extension of the Standard Model

In the context of a gauge invariant, nonanomalous, and family-dependent (nonuniversal) $U(1{)}^{\prime }$ extension of the Standard Model, wherein a new high-scale mechanism generates masses and couplings for the first two fermion generations and the standard Higgs mechanism does so for the third one, we find solutions to the anomaly observed by the Atomki Collaboration in the decay of excited states of beryllium, in the form of a very light $Z^{\prime }$ state, stemming from the $U(1{)}^{\prime }$ symmetry breaking, with significant axial couplings so as to evade a variety of low-scale experimental constraints.

Figure 1

Allowed parameter space mapped on the $(g^{\prime },\tilde{g})$ plane explaining the anomalous ${}^8{\mathrm{Be}}^{*}$ decay for $Z^{\prime }$ solutions with mass 16.7 (red), 17.3 (purple), and 17.6 (green) MeV. The white regions are excluded by the nonobservation of the same anomaly in the ${{}^8\mathrm{Be}}^{{*}^{\prime }}$ transition. Also shown are the constraints from $(g-2{)}_{\mu }$, to be within the two dashed lines; $(g-2{)}_e$, to be inside the two dotted lines (shaded in blue); and the electron beam dump experiment, NA64, to be in the shaded blue region outside the two solid lines. The surviving parameter space lies at small positive and negative $\tilde{g}$ (though not at $\tilde{g}=0$), inside the dark shaded blue region which overlaps the Atomki anomaly solutions.

Figure 2

Values of the upper limit Br (lower limits are smaller than the scale of the plot), as defined in Eq. (23), versus the mass of the $Z^{\prime }$ obtained scanning over the allowed parameter space in $(g^{\prime },\tilde{g})$, obtained from Fig. 1 for each mass step taken (in blue). The Atomki Collaboration solutions are also shown (in orange).