Decoding Heavy Top-Philic Resonances at the HL-LHC: From Parton Kinematics to Deep Learning Signatures

The stabilization of the electroweak scale strongly motivates the search for new heavy resonances and top-partner states. We investigate the discovery potential of exotic resonances mediating the production of vector-like quarks at the High-Luminosity LHC ($\sqrt{s}=13.6$ TeV), focusing on the $pp\to X\to t{\bar{t}}_p$ cascade decay. Using a model-independent Effective Field Theory approach, we classify the intermediate mediator $X$ by its spin (0 and 1) and color (singlet and octet) representations. Parton-level kinematics demonstrate that the normalized differential cross-section with respect to the transverse momentum provides a robust observable for spin discrimination. To address the experimental challenges of highly boosted, semi-resolved hadronic decays, we introduce a cut-flow strategy based on an inclusive four-jet invariant mass reconstruction, $M(4j)$. Because this standard approach remains sensitive to systematic uncertainties, we implement a Generalized BSM Tagger based on Deep Neural Networks (DNNs). By exploiting non-linear multi-jet correlations, the DNN achieves robust background rejection factors ranging from $\mathcal{O}(600)$ to $\mathcal{O}(1000)$ while preserving the underlying partonic signatures. Projecting to an integrated luminosity of $3000{\text{ fb}}^{-1}$, this combined strategy yields a projected statistical significance of $3.74\sigma$ for the dominant color-octet vector channel, establishing strong evidence potential and offering a robust phenomenological baseline for future HL-LHC searches.