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

Abstract

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 predominantly decays into $Wb$, with production cross sections peaking at 9.16~TeV and decreasing above 3~TeV due to parton distribution functions (PDFs) and phase-space suppression. Sensitivity is enhanced through optimized kinematic selections, with the hadronic channel providing higher event rates due to the larger hadronic branching fraction of the $W$ boson, while the leptonic channel offers a cleaner background environment. At an integrated luminosity of 3000~fb$^{-1}$, a 3~TeV $T$ quark can be observed with statistical significances of $21.86\sigma$ and $3.75\sigma$ in the hadronic and leptonic channels, respectively. A machine-learning analysis employing a Boosted Decision Tree (BDT) and a Multi-Layer Perceptron (MLP) is performed at 9.16~TeV for $m_T = 3000$~GeV using $S/B$ and $S/\sqrt{S+B}$ as performance metrics. The MLP consistently outperforms the BDT, achieving a hadronic purity gain of approximately 2.62 while maintaining stable performance across all luminosities. These results demonstrate that a future muon-proton collider can probe vector-like $T$ quark masses up to approximately 3.5~TeV, significantly extending the search for physics beyond the Standard Model.