Naturally realized two dark $Z$’s near the electroweak scale

Chiral representations are the key to obtaining light fermions from some ultraviolet completed theories. The well-known chiral example is one family set of 15 chiral fields in the standard model. We find a new chiral theory ${\mathrm{SU}(2)}_{\mathrm{dark}}\times \mathrm{U}(1{)}_Q$ with 16 chiral fields, which does not have any gauge and gravitational anomalies. The group ${\mathrm{SU}(2)}_{\mathrm{dark}}\times \mathrm{U}(1{)}_Q$ may belong to the dark sector, and we present a derivation of the spectrum from the ${\mathrm{E}}_8\times {\mathrm{E}}_8^{\prime }$ heterotic string. Necessarily, there appear two degrees at low energy: two dark-$Z^{\prime }$’s, or a dark-$Z^{\prime }$ plus a dark photon. Being chiral, there is a chance to probe this theory at TeV accelerators. Since the model belongs to the dark sector, the way to probe it is through the kinetic mixing.

Figure 1

The red dashed line is for ${\mathrm{SU}(2)}^{\prime }$.