Probing Singlet Vector‑Like Top Quarks in the Hadronic tZ (Z→νν̄) Channel at the HL‑LHC using Machine and Deep Learning Architectures

 We study single production of a vector‑like singlet top partner T at the 14 TeV HL‑LHC in the channel pp → Tj with T → tZ, t → bW → bjj, and Z → νν̄. Signal and background samples are generated with MadGraph5_aMC@NLO v3.5.11, showered with Pythia 8, and passed through Delphes. The dominant backgrounds are tt̄, tZj, ZZjj, and WZjj (including charge conjugates). A hadronic pre‑selection (Nj ≥ 3, Nb ≥ 1, Nl = 0) is imposed as trigger, followed by optimized kinematic cuts. We perform multivariate classification with Extreme Gradient Boosting (XGBoost) and a Graph Neural Network (GNN) using jet‑level features. Sensitivities at 3000 fb−1 are quoted using the Asimov significance, S/√(S+B), and an Asimov variant including a 20% background systematic. The model parameters g* and RL are defined in the text, and a single global working point is used to avoid per‑mass tuning bias. In the (g*, mT) scan we present 2σ exclusion and 5σ discovery contours for RL = 0 and RL = 0.5. For RL0, 2σ exclusion corresponds to g* in [0.17, 0.49] ([0.16, 0.43] for GNN) over mT in [1.8, 2.7] TeV, while 5σ discovery corresponds to g* in [0.27, 0.44] ([0.26, 0.40]) over mT in [1.8, 2.2] TeV. For RL = 0.5, the 2σ reach is g* in [0.21, 0.48] ([0.20, 0.43]) over mT in [1.8, 2.5] TeV, and the 5σ reach is g* in [0.33, 0.43] ([0.31, 0.49]) over mT in [1.8, 2.2] TeV, with the GNN yielding slightly stronger and smoother limits across the scan.