Signal of four muons or more from a vector-like lepton decaying to a muon-philic Z′ boson at the LHC

We propose a novel possibility to detect a very distinctive signal with more than four muons originating from pair-produced vector-like leptons decaying to a muon-philic ${Z}^{\ensuremath{'}}$ boson. These new particles are good candidates to explain the anomalies in the muon anomalous magnetic moment and the $b\ensuremath{\rightarrow}s\ensuremath{\ell}\ensuremath{\ell}$ processes. The doublet (singlet) vector-like leptons lighter than 1.3 (1.0) TeV are excluded by the latest data at the LHC if $\mathrm{BR}(E\ensuremath{\rightarrow}{Z}^{\ensuremath{'}}\ensuremath{\mu})=1$. We also show that the excess in the signal region with more than five leptons can be explained by this scenario if the vector-like lepton is a weak singlet, with mass about 400 GeV and $\mathrm{BR}(E\ensuremath{\rightarrow}{Z}^{\ensuremath{'}}\ensuremath{\mu})=0.25$. The future prospects at the HL-LHC are discussed.