Search for the vectorlike leptons in the U(1)$_X$ model inspired by the $B$-meson decay anomalies

We consider the $\text{U}(1)_X$ model, which can induce the flavor violating couplings through vector-like fermions and address the observed rare $B$-meson decay anomalies. To be consistent with all the other observations, both the associated gauge boson mass and the vector-like lepton mass are bounded from above. We argue that the search for new vector-like leptons is promising and provides a complement to the $Z'$ search. A detailed collider analysis shows that the model with the vector-like lepton mass up to 1000 GeV could be tested at the future LHC.