A Redux on "When is the Top Quark a Parton?"

TL;DR

This paper reevaluates the importance of resumming collinear singularities via top quark PDFs in high-energy proton-proton collisions, finding the effect to be generally small under typical collider conditions.

Contribution

It demonstrates that the impact of top quark PDFs in associated production processes is often negligible at high energies, challenging previous assumptions.

Findings

Top PDF effects are small at sqrt(S) ~ 100 TeV.

The effect is suppressed by phase space and small alpha_s.

In many cases, bottom PDFs have a larger impact than top PDFs.

Abstract

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.