Complete vectorlike fourth family and new ${\mathrm{U}(1)}^{\prime }$ for muon anomalies

We consider the Standard Model (SM) with the addition of a $\mathrm{U}(1{)}^{\prime }$ gauge symmetry and a complete fourth family of quarks and leptons which are vectorlike with respect to the full $\mathrm{SU}(3{)}_{\mathrm{C}}\times \mathrm{SU}(2{)}_{\mathrm{L}}\times \mathrm{U}(1{)}_{\mathrm{Y}}\times \mathrm{U}(1{)}^{\prime }$ gauge symmetry. The model provides a unified explanation of experimental anomalies in $(g-2{)}_{\mu }$ as well as $b\to s{\ell }^{+}{\ell }^{-}$ decays. We find good fits to the deviations from the SM, while at the same time fitting all other SM observables. The model includes a new $Z^{\prime }$ gauge boson, a $\mathrm{U}(1{)}^{\prime }$-breaking scalar, and vectorlike leptons all with mass of order a few hundred giga-electron-volts. It is consistent with all currently released high energy experimental data; however, it appears imminently testable with well-designed future searches. Also, precision flavor experiments, especially more accurate direct determinations of Cabibbo-Kobayashi-Maskawa matrix elements, would allow probing the best fit points.

Figure 1

Scale of the $\mathrm{U}(1{)}^{\prime }$ Landau pole as a function of $g^{\prime }$ at 1 TeV.

Figure 2

The muon mass $m_2$ and ${\delta }_{Z^{\prime }}{a}_{\mu }$ in dependence of ${\lambda }_e$ and ${\lambda }_e^{\prime }$.