Abstract
Whilst the prospect of new Z′ gauge bosons with only axial couplings to the Standard Model (SM) fermions is widely discussed, examples of anomaly-free renormalisable models are lacking in the literature. We look to remedy this by constructing several motivated examples. Specifically, we consider axial vectors which couple universally to all SM fermions, as well as those which are generation-specific, leptophilic, and leptophobic. Anomaly cancellation typically requires the presence of new coloured and charged chiral fermions, and we argue that in a large class of models masses of these new states are expected to be comparable to that of the axial vector. Finally, an axial vector mediator could provide a portal between SM and hidden sector states, and we also consider the possibility that the axial vector couples to dark matter. If the dark matter relic density is set due to freeze-out via the axial vector, this strongly constrains the parameter space.
Highlights
Couplings between chiral fermions fL, fR and a vector boson Z associated to a U(1) gauge symmetry are of the form f D/ f =f γμ ∂μ − ig(qfL + qfR) 2 Z μ qfR ) γ5 2 Z μ f. (1)
Axial vectors have been motivated in a number of different contexts
Whilst many studies consider scenarios with axial vector gauge bosons, they often neglect to confront the challenges of anomaly cancellation
Summary
Couplings between chiral fermions fL, fR and a vector boson Z associated to a U(1) gauge symmetry are of the form f D/ f =f γμ. The breaking pattern may include U(1) factors and anomaly cancellation can be inherited from the matter content under the larger gauge group, as in the case of the 27 of E6 under its axial subgroup U(1)ψ [14]. This paper is structured as follows: In Section 2 we discuss the requirements for anomaly cancellation when the gauge structure of the SM is supplemented with a new U(1) factor, focusing on the case in which the U(1) gauge boson has only axial vector couplings to the SM fermions (and DM). We use these techniques to identify a number of anomaly free spectra for axial vector models of interest. We show alternative sets of anomaly free sets of fermions with axial vector Z in Appendix B and we give an explicit example of the algebraic constructions of anomaly free spectra in Appendix C
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