  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 $gg\to t\bar t H$ in comparison with $t\bar t \to H$ and $tg\rightarrow
tH$ 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 $m_H\approx$ 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 $t\bar t\to H$ 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.
