Searching for single production of vectorlike quarks decaying into Wb at a future muon-proton collider

This work investigates the discovery potential for singly produced vectorlike quarks~(VLQs) $T$ ($Q=+2/3e$) and $Y$ ($Q=-4/3e$) decaying to $Wb$ at future $\mu p$ colliders with $\sqrt{s}=5.29$, 6.48, and 9.16 TeV, analyzing both leptonic and hadronic $W$ decay channels through detailed detector simulations. The hadronic channel demonstrates superior sensitivity, enabling $5\sigma$ discovery up to $m_T=3750$ GeV ($m_Y=4100$ GeV) at 9.16 TeV with 100 fb$^{-1}$, while exclusion limits reach $m_T=4500$ GeV ($g^*\geq0.06$) and $m_Y=4800$ GeV ($\kappa_Y\geq0.04$) - significantly beyond LHC capabilities. At 5.29 TeV, discovery regions cover $g^*\in[0.15,0.5]$ for $m_T\in[1500,2520]$ GeV and $\kappa_Y\in[0.12,0.5]$ for $m_Y\in[1700,2700]$ GeV, with exclusions extending to $m_T=2750$ GeV and $m_Y=3020$ GeV. These results, obtained within a simplified two-parameter framework ($m_{T/Y}$ and electroweak couplings $g^{\ast}$), establish $\mu p$ colliders as uniquely powerful tools for probing high-mass VLQ states, particularly in the boosted jet regime.