Axial Vector $Z'$ and Anomaly Cancellation

TL;DR

This paper constructs anomaly-free models of axial vector Z' bosons coupling to Standard Model fermions, exploring their implications for dark matter interactions and the necessity of new chiral fermions.

Contribution

It provides the first explicit examples of anomaly-free axial Z' models with various coupling schemes, including generation-specific and dark matter interactions.

Findings

Anomaly cancellation requires new chiral fermions with masses comparable to the Z'

Models can include couplings to dark matter, constraining parameter space

Axial vectors can serve as portals between SM and hidden sectors

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.