Naturally realized two dark Z's near the electroweak scale

Chiral representations are the key in obtaining light fermions from some ultra-violet completed theories. The well-known chiral example is one family set of fifteen chiral fields in the standard model. We find a new chiral theory SU(2)${}_{\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{k}}\times$U(1)${}_Q$ with sixteen chiral fields, which does not have any gauge and gravitational anomalies. The group SU(2)$_{\rm dark}\times$U(1)$_Q$ may belong to the dark sector, and we present a derivation of the spectrum from the E${}_8\times$E${}_8^{\mathrm{\prime }}$ hetrotic string. Necessarily, there appear two degrees at low energy: two dark Z’s, or a dark Z 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.