Redux on "when is the top quark a parton?"

If a new heavy particle φ is produced in association with the top quark in a hadron collider, the production cross section exhibits a collinear singularity of the form log(mφ/mt), 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 S∼100 TeV due to three factors: (1) αs at the scale μ=mφ, which is quite small when log(mφ/mt) is large, (2) the Bjorken x≪1 for mφ≲10 TeV, and (3) the kinematic region where log(mφ/mt)≫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 bφ. However, in the pT distribution of the charged Higgs, the NLL calculation using a top PDF is crucial to generate the pT distribution for pT≲mt.