The strongest projection comes from an arXiv preprint studying whether a future muon-proton collider could discover a hypothetical heavy T quark through its decay to a top quark and a Z boson. At a center-of-mass energy of 9.16 TeV, the projected 5σ region, the study's discovery threshold, covers T masses from 1,500 to 3,100 GeV and effective couplings from 0.09 to 0.5, assuming 1,000 fb−1 of integrated luminosity and 20% systematic uncertainty. The same study reports a projected 95% confidence-level exclusion region reaching 3,700 GeV, with couplings from 0.06 to 0.5. These are simulation-based projections, not an observed discovery.
The paper asks whether a singly produced vector-like top quark T can be discovered in the T to tZ channel at a future muon-proton collider. The particle is treated as a hypothetical heavy quark labeled T, and the benchmark is one specific test case: a singlet vector-like T quark under SU(2)L. The study evaluates three collider scenarios with center-of-mass energies of 5.29, 6.48 and 9.16 TeV.
How the search was modeled
The analysis is built from simulated signal events and irreducible Standard Model backgrounds for the baseline topology. Events are generated at leading order, then passed through Pythia 8.3 for showering and hadronization, Delphes 3.4.2 for detector simulation using the standard LHeC detector card, and MadAnalysis 5 for the analysis.
At the benchmark point g* = 0.1 and a T mass of 2 TeV, the modeled T to tZ cross section is 0.19 femtobarns at 5.29 TeV, 0.61 femtobarns at 6.48 TeV and 2.74 femtobarns at 9.16 TeV. The study says the single-production cross section scales with the square of g*, the model's effective coupling.
The selection then narrows the event sample sharply. It requires a fat jet, meaning a large reconstructed jet, above 400 GeV whose mass is within 10 GeV of the Z-boson mass, an isolated lepton and a b-tagged top-decay jet. The leading jet's transverse momentum must exceed 150 GeV, its angular separation from the lepton must be below 1.0, and the reconstructed system mass must exceed 800 GeV. After all cuts, the reported total Standard Model background cross sections are 0.0078 fb at 5.29 TeV, 0.014 fb at 6.48 TeV and 0.029 fb at 9.16 TeV, while signal efficiencies remain at the percent level.
The reach comes with caveats
With the default 20% systematic uncertainty, the projected 5σ discovery region at 5.29 TeV spans couplings from 0.16 to 0.5 and T masses from 1,500 to 2,200 GeV. At 6.48 TeV, the ranges become 0.12 to 0.5 and 1,500 to 2,500 GeV. At 9.16 TeV, they reach 0.09 to 0.5 and 1,500 to 3,100 GeV. The study also presents a zero-systematics comparison. Overall, the higher-energy scenarios extend the reported reach to heavier T masses and weaker couplings.
At g* = 0.5, the corresponding projected 5σ mass limits are 2,200, 2,500 and 3,100 GeV, while the 95% confidence-level exclusion limits are 2,500, 3,000 and 3,700 GeV across the 5.29, 6.48 and 9.16 TeV scenarios. The authors describe the T to tZ and T to Wb channels as complementary search signatures.
The reported sensitivity is restricted to relative T-quark widths up to approximately 50%, with relative width meaning the modeled width compared with the T mass. A complete off-shell calculation that includes interference is deferred. The paper also does not carry out full detector simulations or significance calculations for alternative T to tZ topologies, and suggests multivariate or advanced jet-substructure studies for those cases.
The document also contains internal inconsistencies that matter when reading the ranges: the supplied analysis flags a conflicting 9.16 TeV exclusion interval and an inconsistency in one 5.29 TeV cut-flow entry. The results are projections from a leading-order sensitivity study, not measurements from collider data. The document is an arXiv version 1 preprint dated 28 Aug 2026, and the projected reach applies to one singlet benchmark and the stated detector and systematic assumptions.
Paper data and sources
Original title: Searching for vectorlike $T$ quarks in the $T\to tZ$ channel at a future muon-proton collider
Authors: Yin-Hao Gao, Yao-Bei Liu
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text