The $tthh$ production at colliders contain rich information on the nature of Higgs boson. In this article, we systematically studied its physics at High-Luminosity Large Hadron Collider (HL-LHC), using exclusive channels with multiple ($geq 5$) $b$-jets and one lepton ($5b1ell$), multiple ($geq 5$) $b$-jets and opposite-sign di-lepton ($5b2ell$), same-sign di-lepton (SS2$ell$), multiple leptons (multi-$ell$), and di-tau resonance ($tautau$). The scenarios analyzed include: (1) the $tthh$ production in Standard Model; (2) the $tthh$ production mediated by anomalous cubic Higgs self-coupling and $tthh$ contact interaction; (3) heavy Higgs ($H$) production with $tt H to tthh$; and (4) pair production of fermionic top partners ($T$) with $T T to tthh$. To address the complication of event topologies and the mess of combinatorial backgrounds, a tool of Boosted-Decision-Tree was applied in the analyses. The $5b1ell$ and SS2$ell$ analyses define the two most promising channels, resulting in slightly different sensitivities. For non-resonant $tthh$ production, a combination of these exclusive analyses allows for its measurment in the SM with a statistical significance $sim 0.9sigma$ (with $S/B > 1 %$), and may assist partially breaking the sensitivity degeneracy w.r.t. the cubic Higgs self-coupling, a difficulty usually thought to exist in gluon fusion di-Higgs analysis at HL-LHC. These sensitivities were also projected to future hadron colliders at 27 TeV and 100 TeV. For resonant $tthh$ productions, the heavy Higgs boson in type II Two-Higgs-Doublet-Model could be efficiently searched for between the mass thresholds $2 m_h < m_H < 2 m_t$ and even beyond that, for relatively small $tanbeta$, while the fermionic top partners in composite Higgs models could be probed for up to $sim 1.5$ TeV and $sim 1.7$ TeV, for Br$(Tto th)=25%$ and $50%$, respectively.
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