Purely flavor-changing Z' bosons and where they might hide

A plethora of ultraviolet completions of the Standard Model have extra U(1) gauge symmetries. In general, the associated massive $Z^\prime$ gauge boson can mediate flavor-changing neutral current processes at tree level. We consider a situation where the $Z^\prime$ boson couples solely via flavor-changing interactions to quarks and leptons. In this scenario the model parameter space is, in general, quite well constrained by existing flavor bounds. However, we argue that cancellation effects shelter islands in parameter space from strong flavor constraints and that these can be probed by multipurpose collider experiments like ATLAS or CMS as well as LHCb in upcoming runs at the LHC. In still allowed regions of parameter space these scenarios may help to explain the current tension between theory and experiment of $(g-2)_\mu$ as well as a small anomaly in $\tau$ decays.