Single production of an exotic vector-like $Y$ quark at future high energy $pp$ colliders

Vector-like quarks have been predicted in various new physics scenarios beyond the Standard Model (SM). In a simplified modelling of a $(B,Y)$ doublet including a vector-like quark $Y$, with charge $-\frac{4}{3}$e, there are only two free parameters: the $Y$ coupling $\kappa_{Y}$ and mass $m_Y$. In the five flavor scheme, we investigate the single production of the $Y$ state decaying into $Wb$ at the Large Hadron Collider (LHC) Run-III and High-Luminosity LHC (HL-LHC) operating at $\sqrt{s}$ = 14 TeV, the possible High-Energy LHC (HE-LHC) with $\sqrt{s}$ = 27 TeV as well as the Future Circular Collider in hadron-hadron mode (FCC-hh) with $\sqrt{s}$ = 100 TeV. Through detailed signal-to-background analyses and detector simulations, we assess the exclusion capabilities of the $Y$ state at the different colliders. We find that this can be improved significantly with increasing collision energy, especially at the HE-LHC and FCC-hh, both demonstrating an obvious advantage with respect to the HL-LHC in the case of high $m_Y$. Assuming a 10\% systematic uncertainty on the background event rate, the exclusion capabilities are summarized as follows: (1) the LHC Run-III can exclude the correlated regions of $\kappa_{Y} \in [0.06,0.5]$ and $m_{Y} \in [1500\text{ GeV},3800\text{ GeV}]$ with integrated luminosity $L = 300\text{ fb}^{-1}$; (2) the HL-LHC can exclude the correlated regions of $\kappa_{Y} \in [0.05,0.5]$ and $m_{Y} \in [1500\text{ GeV},3970\text{ GeV}]$ with $L = 3$ ab$^{-1}$; (3) the HE-LHC can exclude the correlated regions of $\kappa_Y \in [0.06,0.5]$ and $m_{Y} \in [1500\text{ GeV} , 6090\text{ GeV}]$ with $L = 3$ ab$^{-1}$; (4) the FCC-hh can exclude the correlated regions of $\kappa_{Y} \in [0.08,0.5]$ and $m_{Y} \in [1500\text{ GeV} , 10080\text{ GeV}]$ with $L = 3$ ab$^{-1}$.