We describe a method to couple $Z^{\prime }$ gauge bosons to the standard model (SM), without charging the SM fields under the $U(1{)}^{\prime }$, but instead through effective higher-dimension operators. This method allows complete control over the tree-level couplings of the $Z^{\prime }$ and does not require altering the structure of any of the SM couplings, nor does it contain anomalies or require introduction of fields in nonstandard SM representations. Moreover, such interactions arise from simple renormalizable extensions of the SM—the addition of vectorlike matter that mixes with SM fermions when the $U(1{)}^{\prime }$ is broken. We apply effective $Z^{\prime }$ models as explanations of various recent anomalies: the D0 same-sign dimuon asymmetry, the CDF $W+\mathrm{di}\mathrm{\text{−}}\mathrm{jet}$ excess and the CDF top forward-backward asymmetry. In the case of the $W+\mathrm{di}\mathrm{\text{−}}\mathrm{jet}$ excess we also discuss several complementary analyses that may shed light on the nature of the discrepancy. We consider the possibility of non-Abelian groups, and discuss implications for the phenomenology of dark matter as well.

• Received 11 May 2011

DOI:https://doi.org/10.1103/PhysRevD.84.115006