A 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 sqrt(S) ~ 100 TeV due to three factors: 1) alpha_s at the scale mu = m_phi is quite small when log(m_phi/m_t) is large, 2) the Bjorken x << 1 for m_phi < ~10 TeV, and 3) the kinematic region where log(m_phi/m_t) >> 1 is suppressed by phase space. We show that the effect of a top PDF is generically smaller than that of a bottom PDF in the associated production of b phi and consider the example of pp -> t H+ at next-to-leading logarithm order.