In Search of an Invisible $Z^\prime$

TL;DR

This paper investigates a class of anomaly-free, potentially flavor non-universal $U(1)_X$ gauge symmetries with a $Z'$ boson that is largely invisible to precision electroweak tests, but constrained by collider searches and anomaly cancellation.

Contribution

It demonstrates that such $Z'$ models cannot evade collider bounds if they are anomaly-free, especially due to the necessity of charged valence quarks and leptons, limiting their invisibility.

Findings

$Z'$ bosons are constrained by LHC dilepton and dijet searches.

FCC-ee and HL-LHC provide complementary coverage of $Z'$ parameter space.

Anomaly cancellation requires valence quarks and leptons to be charged under $U(1)_X$.

Abstract

We consider extending the Standard Model by an anomaly-free and possibly flavour non-universal $U(1)_X$ gauge symmetry, whose breaking gives a $Z^\prime$ boson that does not affect electroweak precision observables at tree-level or via 1-loop renormalisation group (RG) running. Provided it does not also couple to electrons, such a $Z^\prime$ boson would be largely invisible to an electroweak precision machine like FCC-ee or CEPC (up to small finite 1-loop matching contributions that we quantify). We show that, while this class of $Z^\prime$ models can also evade tests of quark flavour violation, the constraint of anomaly-cancellation implies that valence quarks, muons, and taus are all charged under $U(1)_X$, with the up quark charge being necessarily large. The conclusion holds even if one augments the SM by three right-handed neutrinos to try and absorb anomalies. This means such $Z^\prime$ bosons cannot simultaneously hide below the TeV scale from $pp \to \ell\ell$ Drell--Yan measurements at the LHC and, even if we entertain esoteric models in which the lepton charges are numerically very small, we cannot escape dijet searches at the LHC. For equitable quark and lepton charges, $pp\to\ell\ell$ already excludes such a $Z^\prime$ up to $M/g \gtrsim$ 10 TeV, with a reach of 20 TeV expected by the end of the High-Luminosity LHC. The dijet bounds currently sit around 5 TeV, while sensitivity up to 10 TeV could be achieved at HL-LHC. We thus find an excellent complementarity between FCC-ee and HL-LHC in covering all anomaly-free $Z^\prime$ bosons up to several TeV.