Searching for single production of a vector-like $Y$ quark decaying into $bW$ at the FCC-eh

We investigate the exclusion and discovery potential for single production of a vector-like $Y$ quark with electric charge $Q=-4/3$, followed by the decay $Y\to bW$, at the FCC-eh. The $Y$ quark is allowed to couple to both first- and third-generation down-type quarks. The analysis is performed for an electron-beam polarization of $P_e=-80\%$ at $\sqrt{s}=3.46$, $5.29$, and $6.9~\mathrm{TeV}$. Both leptonic and hadronic $W$-boson decay channels are considered. In the hadronic channel, the boosted $W$-boson is reconstructed as a $W$-jet, and kinematic observables are used to suppress the Standard Model (SM) backgrounds. By performing a detailed detector simulations and event analysis, we present the $2\sigma$ exclusion limits and $5\sigma$ discovery reaches in the $g^*$--$m_Y$ plane, where $g^*$ is $Y$ coupling strength to the SM quarks. We find that the hadronic channel can provide stronger exclusion and discovery sensitivities, which are improved with increasing $\sqrt{s}$ at the FCC-eh.