The Weinberg Angle Without Grand Unification

Abstract

We assume that strong and electroweak interactions become strong at very high energies. With this assumption, we compute the low-energy gauge coupling constants $\alpha_i (m_Z)$ as a function of the cutoff scale, taking the supersymmetric standard model with $3+2n$ families of quark and lepton multiplets. We find that only the five family case $(n=1)$ is consistent with the experimental values of the gauge coupling constants. This suggests the presence of a pair of families at $\sim 1$~TeV.