$Z^{\prime }$ Phenomenology: A Model-independent Analysis and Fit in Combination of Chiral Effective Theory and Anomaly Cancellation

Abstract

To investigate $Z^{\prime }$ phenomenology model-independent, we combine chiral effective theory with anomaly cancellation conditions without any other model input. We focus on $Z^{\prime }$ mixings with $\gamma -Z$ in both mass and kinetic parts and calculate contributions to oblique $S,T,U$. The three sets of anomaly-free fermion $U(1{)}^{\prime }$ charges parameterize the $Z^{\prime }$ interactions with fermions. The cancellation of the $[U(1{)}^{\prime }{]}^3$ anomaly and mixing gravitational-gauge anomaly determines the number of right-handed neutrinos. We also find a novel relation between the charge assignments and Stueckelberg coupling in terms of the renormalized electromagnetic current. A global fit to the electroweak precise observables shows that typical values for the mixing parameters are of order $10^{-3}$. In spite of this strict limit, we obtain a negative $S$ parameter contribution.

Comments: 23 pages, 6 figues, 2 tables