$t\bar{t}$ spin correlations from toponium production scenarios to non-relativistic resummation beyond the standard perturbative baseline
$t\bar{t}$ spin correlations originating from theoretical models assuming on one side toponium bound state formation in proton-proton collisions at 13 TeV are compared against predictions from non-relativistic QCD ressumation effects via Green's function formalism that go beyond the perturbative $t\bar{t}$ baseline with no bound state but could justify extra yield of events in the $t\bar{t}$ mass spectrum recently observed by ATLAS and CMS Collaborations, still awaiting an explanation. Toponium production comprises two scenarios, a simplified Effective Field Theory (EFT) with $η_t\rightarrow t\bar{t}$ decays and an additional model with scalar and vector toponium states with $η_t\rightarrow HZ$ and $J_t\rightarrow ZW^+W^-$ decays. Experimental measurements on $t\bar{t}$ system are added to the comparisons. Fitted diagonal spin correlation $C_{kk}$, $C_{rr}$, $C_{nn}$ matrix terms show a relative increase in value ranging from 200%-2330% for toponium $t\bar{t}$ decays with respect the perturbative NLO baseline. Relative contribution from resummation effect ranges from 0.6% to 10.4% and its combination with perturbative baseline improves agreement with Data distributions, with $χ^2/N_\mathrm{dof}$ value reduced by $\sim$4.5%-60.0% . Equivalent fitted cross-section for resummation effect $σ_{res}$, ranges from 7.3 to 9.1 pb in consistency with excess yield reported by LHC experiments. $σ_{res}$ $>$ 50 pb range is excluded at 95% C.L. A classifier performing at detector level achieves a ROC curve area of $0.91$ leading to toponium signal to background significances over 55. These results indicate that efficient isolation of observed $t\bar{t}$ excess events from background is feasible and a characterisation via spin correlation measurements would reveal their consistency with either toponium production or non-relativistic effects beyond the perturbative baseline.