Probing the pair production of first-generation vector-like leptons at future $e^+e^-$ colliders

This work explores the discovery potential of the first-generation weak isosinglet Vector-Like Leptons (VLLs), denoted by $E^\pm$, via pair production at future electron-positron colliders. Our analysis adopts a comprehensive framework that incorporates beam polarization configurations and leverages detailed detector simulations. We focus on two distinct multilepton signatures: the $2\ell + 2j + \slashed{E}_T$ and $3\ell + 2j + \slashed{E}_T$ final states ($\ell = e, \mu$). Both signatures arise from the decay $E^{\pm} \to Z e^{\pm} / W^{\pm} \nu_\ell$ and are distinguished by the decay patterns of the associated gauge bosons. By applying optimized selection criteria to both signal and background events, we establish exclusion sensitivities and discovery prospects across the VLL mass spectrum. Our findings demonstrate that, for integrated luminosities of $\SI{25}{fb^{-1}}$, $\SI{90}{fb^{-1}}$ and $\SI{1000}{fb^{-1}}$ at corresponding center-of-mass (c.m.) energies of $\SI{1}{TeV}$, $\SI{1.5}{TeV}$ and $\SI{3}{TeV}$, the accessible mass range extends to approximately $\SI{490}{GeV}$, $\SI{740}{GeV}$ and $\SI{1440}{GeV}$, which represents a substantially improvement over the detection limits of existing hadron collider experiments.