We argue that in models with several high scales; e.g. in composite Higgs models or in gauge extensions of the Standard Model (SM), vector-like leptons can be likely produced in a relatively large $sqrt{s}$ region of the phase space. Likewise, they can easily decay into final states not containing SM gauge bosons. This contrasts with the topology in which these new particles are being searched for at the LHC. Adopting an effective field theory approach, we show that searches for excited leptons must be used instead to test this scenario. We derive bounds on all the relevant interactions of dimension six; the most constrained ones being of about $0.05$ TeV$^{-2}$. We build new observables to improve current analyses and study the impact on all single-field UV completions of the SM extended with a vector-like lepton that can be captured by the effective field theory at tree level, in the current and in the high-luminosity phase of the LHC.
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