Search for the singlet vector-like lepton at future $$e^+ e^-$$ colliders

Searching for the new particles beyond the standard model (SM) is an important way to probe new physics beyond the SM. In one class of new particles there are nonchiral color singlet fermions that couple to the SM leptons, that is vector-like leptons (VLLs), which have been widely concerned in experiment and theory. The existing literature shows that the singlet VLLs suffer from a big difficult challenge for discovery at future proton-proton colliders. In this paper, we study the prospects of searching for the singlet VLLs in pure leptonic and fully hadronic channels at $$e^+ e^-$$ colliders. We find that there is an opportunity for excluding the region $$m_{\tau ^{\prime \pm }} \in $$ [180 GeV, 240 GeV] with $${\mathcal {L}}$$ $$\in $$ [ $$3.0\hbox { fb}^{-1}$$ , $$14.9\hbox { fb}^{-1}$$ ] ([ $$0.1\hbox { fb}^{-1}$$ , $$0.3\hbox { fb}^{-1}$$ ]) at ILC of $$\sqrt{s} = 500\ \hbox { GeV}$$ , the region $$m_{\tau ^{\prime \pm }} \in $$ [240 GeV, 450 GeV] with $${\mathcal {L}} \in $$ [ $$9.9\hbox { fb}^{-1}$$ , $$23.1\hbox { fb}^{-1}$$ ] ([ $$0.2\hbox { fb}^{-1}$$ , $$0.3\hbox { fb}^{-1}$$ ]) at ILC of $$\sqrt{s} = 1000\ \hbox { GeV}$$ and the region $$m_{\tau ^{\prime \pm }} \in $$ [450 GeV, 700 GeV] with $${\mathcal {L}} \in $$ [ $$52.1\hbox { fb}^{-1}$$ , $$197.9\hbox { fb}^{-1}$$ ] ([ $$2.21\hbox { fb}^{-1}$$ , $$4.5\hbox { fb}^{-1}$$ ]) at CLIC of $$\sqrt{s} = 1500\ \hbox {GeV}$$ in the pure leptonic (fully hadronic) channel. It is more optimistic for excluding and discovering the singlet VLL through the fully hadronic channel at future high energy $$e^+ e^-$$ colliders.