Probing Vector-Like Quarks at a future Muon-Proton Collider

This study investigates the discovery potential of a singly produced vector-like top quark ($T$) at a future muon-proton collider with center-of-mass energies of 5.29, 6.48, and 9.16 TeV, using a model-independent effective Lagrangian consistent with CKM and electroweak constraints. The $T$ quark mainly decays into $Wb$, with production cross-sections peaking at 9.16 TeV and decreasing above 3 TeV due to PDFs and phase-space suppression. Sensitivity is enhanced through optimized kinematic cuts, with the hadronic channel providing higher event rates due to the larger $W$ branching into quarks, while the leptonic channel offers cleaner backgrounds. At an integrated luminosity of 3000 fb$^{-1}$, a 3 TeV $T$ quark could be observed with significances of 21.86$\sigma$ in the hadronic channel and 3.75$\sigma$ in the leptonic channel. A machine learning approach using Boosted Decision Trees (BDT) and Multi-Layer Perceptrons (MLP) was employed at 9.16 TeV for $m_T=3000$ GeV, with $S/B$ and $S/(S+B)$ as metrics. The MLP outperformed BDTs across all luminosities, achieving a hadronic purity gain of about 2.62 and demonstrating nearly luminosity-independent stability. These results show that a muon-proton collider can probe $T$ quark masses up to approximately 3.5 TeV, significantly extending the reach of new physics searches beyond current collider capabilities.