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Precise determination of top-quark pairs is an essential tool forunderstanding the overall consistency of the standard model (SM) expectations,understanding limited New Physics (NP) models, through spin-spin correlationand polarization parameters, and has a critical impact on the analysesstrategies at upcoming LHC programs. In this work, we review and discussvarious state-of-the-art Monte Carlo (MC) methodologies as\textsc{MadGraph5}\_aMC@NLO, \textsc{Sherpa}, \textsc{Powheg-Box} and\textsc{Pythia8}, which are Matrix Element (ME)$/$Parton Shower (PS) matchinggenerators including a complete set of spin correlation and polarization in topquark pair production with dileptonic final states. This is the first suchstudy that not only compares the effects of different MC event generatorapproaches on spin density matrix elements and polarization parameters, butalso investigates the effects of leading order (LO) and next-to-leading order(NLO) accuracy in QCD, and electroweak (EW) corrections via \textsc{Sherpa}.Moreover, as a continuation of the work, the prospects for possible NPscenarios through top-quark spin-spin correlation and polarization measurementsfor Supersymmetry (R parity conserved and violated models) and Dark Matter (topquarks associated mediator) models during upcoming LHC runs are brieflyoutlined. We find that all SM MC predictions for the defined set of variablesare generally consistent with the experimental data and theoretical predictionswithin the uncertainty variations. Besides, for the distributions of the$\cos\varphi$, laboratory-frame observables ($\cos\varphi_{lab}$ and$|\Delta\phi_{ll}|$) and the observables generated by parity (P) andcharge-parity (CP) conserving interactions, we conclude some clues that theconsidered signals and beyond may well be separated from experimental data andlocated above the SM predictions.

Comparison of spin-correlation and polarization variables of spin density matrix for top quark pairs at the LHC and New Physics implications