Doubly Charged Lepton Search Potential of the FCC-Based Energy-Frontier Electron-Proton Colliders

We search for the doubly charged leptons ($L^{--}$) predicted in composite models including extended weak isospin multiplets namely, $I_{W}=1$ and $I_{W}=3/2$ at the Future Circular Collider (FCC)-based energy-frontier electron-proton colliders with the center-of-mass energies of $\sqrt{s}=3.46$ TeV, $\sqrt{s}=10$ TeV, and $\sqrt{s}=31.6$ TeV, respectively. We deal with the $e^{-}p\rightarrow L^{--}X\rightarrow e^{-}W^{-}X$ process, calculate the production cross sections and give the normalized transverse momentum and pseudorapiditiy distributions of final state electron to obtain the kinematical cuts for the discovery. We show the statistical significance ($SS$) of the expected signal yield as a function of doubly charged lepton mass ($SS-M_{L}$ plots) to attain the doubly charged lepton discovery mass limits both for the $I_{W}=1$ and $I_{W}=3/2$. It is obtained that discovery mass limits on the mass of doubly charged lepton for $I_{W}=1$ ($I_{W}=3/2$) are, $2.21\,(2.73)$ TeV, $5.46\,(8.47)$ TeV, and $12.9\,(20.0)$ TeV for $\sqrt{s}=3.46$ TeV, $\sqrt{s}=10$ TeV, and $\sqrt{s}=31.6$ TeV, respectively.