Naturally realized two dark Z ’s near the electroweak scale

Abstract

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 ${\mathrm{SU}(2)}_{\mathrm{dark}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{Q}$ with 16 chiral fields, which does not have any gauge and gravitational anomalies. The group ${\mathrm{SU}(2)}_{\mathrm{dark}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{Q}$ may belong to the dark sector, and we present a derivation of the spectrum from the ${\mathrm{E}}_{8}\ifmmode\times\else\texttimes\fi{}{\mathrm{E}}_{8}^{\ensuremath{'}}$ heterotic string. Necessarily, there appear two degrees at low energy: two dark-${Z}^{\ensuremath{'}}$'s, or a dark-${Z}^{\ensuremath{'}}$ 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.