Illuminating long-lived dark vector bosons via exotic Higgs decays at $\sqrt{s} = 13\,{\text {TeV}}$

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.