Redux on When is the top quark a parton?

If a new heavy particle phi is produced in association with the top quark in a hadron collider, the production cross section exhibits a collinear singularity of the form log(m(phi)/m(t)), which can be resummed by introducing a top quark parton distribution function (PDF). We reassess the necessity of such resummation in the context of a high-energy pp collider. We find that the introduction of a top PDF typically has a small effect at root S similar to 100 TeV due to three factors: (1) alpha(s) at the scale mu = m(phi), which is quite small when log(m(phi)/m(t)) is large, (2) the Bjorken x << 1 for m(phi) less than or similar to 10 TeV, and (3) the kinematic region where log(m(phi)/m(t)) >> 1 is suppressed by phase space. We consider the example of pp -> tH(+) at next-to-leading logarithm(NLL) order and show that, in terms of the total cross section, the effect of a top PDF is generically smaller than that of a bottom PDF in the associated production of b phi. However, in the p(T) distribution of the charged Higgs, the NLL calculation using a top PDF is crucial to generate the p(T) distribution for p(T) less than or similar to m(t).