On a standard model extension with vector-like fermions and Abelian symmetry

We investigate an extension of the standard model with vector-like fermions and an extra Abelian gauge symmetry. The particle mass spectrum is calculated explicitly. The Lagrangian terms for all the gauge interactions of leptons and quarks in the model are derived. We observe that while there is no new mixing in the lepton sector, the quark mixing plays an important role in the magnitudes of gauge interactions for quarks, particularly the interactions with massive \(W\), \(Z\) and \(Z'\) bosons. We calculate the contributions of the new vector-like leptons and quarks to the Peskin-Takeuchi parameters as well as the \(\rho\) parameter of the electroweak precision tests, and show that the model is realistic.