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Recently, the vector-like leptons (VLLs) as a simple extension to thestandard model (SM) have attracted widespread attention both in theory andexperiments. The present collider searches mainly focus on the studies of theirprompt decays, which prefer a relatively large coupling. In this paper, weconcentrate on searches for long-lived signatures of the singlet VLLs $F$ ortheir accompanying scalar particles $\phi$ both in the hadronic and electroniccolliders. The long-lived signatures are naturally induced from small chiralmass mixing between VLLs and SM leptons. Two specific models distinguished bywhether the VLLs couple to scalar particles are introduced to realize theaforementioned features. For long-lived VLLs case, we find that with the kinktrack method the sensitivities at future HL-LHC with $\sqrt{s}=13~\text{TeV}$can reach the regions for VLL mass $m_F \in [200,950]~\text{GeV}$ and the massmixing parameter $\theta_L \in [10^{-10},10^{-7}]$. For the long-livedaccompanying scalar particle case, by fixing VLLs or scalar mass, or the massratio between VLL and the accompanying scalar, we explore the projectedsensitivities through the time delay and displaced vertex strategies, which canprobe the regions for $m_F \in [200,1200]~\text{GeV}$ and coupling$y\theta_L\in [10^{-11},10^{-6}]$. Furthermore, we also explore the long-livedaccompanying scalars at the future CEPC provided that the VLLs can couple tothe SM first-generation leptons. We find that CEPC has good performances for$m_\phi < 70~\text{GeV}$ and $m_F<1000~\text{GeV}$. These long-lived searchesare complementary to previous studies, which opens the door towards the smallercoupling regions.

Long-lived Searches of Vector-like Lepton and Its Accompanying Scalar at Colliders