The Weak Mixing Angle From TeV Scale Quark-Lepton Unification

Unified theories based on an extended left-right symmetric group, $SU(4) \times SU(2)^4$, are constructed in five dimensions. The compactification scale is assumed to be only a loop factor above the weak scale, so that the weak mixing angle is predicted to be close to its tree level value of 0.239. Boundary conditions in the 5th dimension break $SU(4) \to SU(3) \times U(1)_{B-L}$,removingpowerfulconstraintsfrom$K_L \to \mu e$ while allowing a reliable calculation of the leading logarithm corrections to ${\sin }^2\theta$. The compactification scale is expected in the 1–5 TeV region, depending on how $SU(2{)}^4$ is broken. Two illustrative models are presented, and the experimental signal of the $Z^{\mathrm{\prime }}$ gauge boson is discussed.