Why should we search for vector-like leptons?

Abstract: There are two strong arguments in favor of vector-like leptons and quarks: Flavor Democracy call for them, and E6 GUT predicts existence of iso-singlet quarks and iso-doublet leptons. Vector-like quarks (VLQ) are extensively searched by ATLAS and CMS collaborations, but this is not the case for vector-like leptons (VLL), while they have actually similar status from phenomenology viewpoint. In this study we argue that vector-like leptons should be included into the new physics search programs of energy-frontier colliders. We consider production of vector-like partners of the first SM family leptons at the HL-LHC, HE-LHC, FCC, ILC, CLIC, Muon Collider, as well as, at ep and {\mu}-p colliders. As for decays of vector-like leptons, we present branching ratios formulas to different channels for the most general case. Since there are many different production and decay channels for charged and neutral vector-like leptons, relevant studies should be done systematically. We invite the High Energy Physics community (both experimenters and phenomenologists) to actively participate in research on this topic.