Distinguishing a pseudoscalar from a vector $t\bar t$ resonance with top-quark spin correlations at the HL-LHC
Top-quark spin correlations provide a direct probe of the quantum numbers of a resonance decaying to $t\bar t$. We compare a CP-odd type-II two-Higgs-doublet-model pseudoscalar $A$ with a spin-1 leptophobic topcolor $Z'$ in the dilepton channel. The two hypotheses differ in the parton-level helicity correlation by $\Delta c_{\rm hel}\simeq0.43$, nearly independently of mass, and neutrino-weighted reconstruction preserves this separation with an effective dilution factor of about 0.66. At 400 and 800 GeV, the pseudoscalar normalization is anchored to CMS HIG-22-013 coupling limits, while the $Z'$ rate is matched to the pseudoscalar so that the comparison primarily tests spin structure. The leading-order $t\bar t$-only projection gives expected separations of 2.27 and 2.74 standard deviations at $3000\,{\rm fb}^{-1}$. Equalizing the selected signal yields gives pure spin-shape separations of 1.86 and 2.70 standard deviations. Profiling a Gaussian-constrained Standard Model $c_{\rm hel}$-shape nuisance gives 2.07 and 2.63 standard deviations for an optimistic sideband benchmark, or 1.67 and 2.26 for a weaker constraint. A local fixed-template extrapolation corresponds to five-standard-deviation discrimination at couplings about 22\% and 16\% above the reference values. A 1500 GeV $g=1$ point is shown separately. The reach is limited by the sub-percent signal fraction and control of the mass-dependent Standard Model spin shape, rather than by the intrinsic resonance-spin separation.