  The possibility of producing a measurable long-lived dark $Z$ boson, that is
assumed to be produced either via its kinetic mixing with the hypercharge gauge
boson or via mixing of the observed 125-GeV Higgs boson with the dark Higgs
boson, called Higgs mixing, in Run 2 of the Large Hadron Collider (LHC) is
investigated. Displaced dimuons in the final state are considered where each of
the $Z$ and the dark $Z$ bosons decays directly to a dimuon. The Higgs
production cross sections via gluon-gluon fusion at 13 TeV calculated to a
combination of next-to-next-to-next-to-leading order with QCD corrections
(N$^{3}$LO QCD) and next-to-leading order with electroweak corrections (NLO EW)
from the literature are used, while the branching fractions are calculated to
NLO by using Monte Carlo simulation in the framework of
{\textsc{MadGraph5}}\_aMC@NLO and compared to the available analytical
calculations to leading order (LO). Sensitivities of the LHC in Run 2 to such
searches are discussed.
