In hadronic collisions at high energies, the top-quark may be treated as a parton inside a hadron. Top-quark initiated processes become increasingly important since the top-quark luminosity can reach a few percent of the bottom-quark luminosity. In the production of a heavy particle $H$ with mass $m_H > m_t$, treating the top-quark as a parton allows us to resum large logarithms $log(m_{H}^{2}/m_{t}^{2}$) arising from collinear splitting in the initial state. We quantify the effect of collinear resummation at the 14-TeV LHC and a future 100-TeV hadron collider, focusing on the top-quark open-flavor process $ggto tbar t H$ in comparison with $tbar t to H$ and $tgrightarrow tH$ at the leading order (LO) in QCD. We employ top-quark parton distribution functions with appropriate collinear subtraction and power counting. We find that (1) Collinear resummation enhances the inclusive production of a heavy particle with $m_Happrox$ 5 TeV (0.5 TeV) by more than a factor of two compared to the open-flavor process at a 100-TeV (14-TeV) collider; (2) Top-quark mass effects are important for scales $m_H$ near the top-quark threshold, where the cross section is largest. We advocate a modification of the ACOT factorization scheme, dubbed m-ACOT, to consistently treat heavy-quark masses in hadronic collisions; (3) The scale uncertainty of the total cross section in m-ACOT is of about 20 percent at the LO. While a higher-order calculation is indispensable for a precise prediction, the LO cross section is well described by the process $tbar tto H$ using an effective factorization scale significantly lower than $m_H$. We illustrate our results by the example of a heavy spin-0 particle. Our main results also apply to the production of particles with spin-1 and 2.
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