Threshold Resummation of the Total Cross Section for Heavy Quark Production in Hadronic Collisions

TL;DR

The paper develops a perturbative threshold resummation framework for heavy quark production in hadronic collisions, focusing on universal leading soft-gluon contributions from initial-state radiation. Using a principal-value resummation approach, it builds a finite, perturbative exponent in moment space and retains only universal leading logarithms to form a resummed partonic cross section, then matches to fixed-order results and delineates a calculable perturbative region via a $z_{max}$ boundary. It delivers all-orders resummed predictions for top-quark production at Tevatron energies, demonstrates reduced scale sensitivity, and compares with other resummation schemes, arguing that restricting to universal leading logs yields reliable results with ~9–10% theoretical uncertainty. The findings align with existing top-quark data within uncertainties and provide a framework applicable to other high-mass processes, with potential improvements from higher-order subleading log mastery. The work offers practical, more stable cross-section predictions for current and future hadron colliders, including the LHC, by controlling non-perturbative effects through a principled perturbative boundary.

Abstract

We discuss calculations of the inclusive total cross section for heavy quark production at hadron collider energies within the context of perturbative quantum chromodynamics, including resummation of the effects of initial-state soft gluon radiation to all orders in the strong coupling strength. We resum the universal leading-logarithm contributions, and we restrict our integrations to the region of phase space that is demonstrably perturbative. We include a detailed comparison of the differences between ours and other methods. We provide predictions of the physical cross section as a function of the heavy quark mass in proton-antiproton reactions at center-of-mass energies of 1.8 and 2.0 TeV, and we discuss estimated uncertainties.

Figures (6)

• Figure 1: Physical cross sections in the $q\bar{q}$ channel as a function of the heavy quark mass, in the $\overline{\rm MS}$ scheme. The solid lines denote the finite-order partial sums of the universal leading-logarithmic contributions from the explicit ${\cal O}(\alpha^3)$ and ${\cal O}(\alpha^4)$ calculations for the $t\bar{t}$ and Drell-Yan processes, respectively. Lower solid: $\sigma^{(0)}$; middle solid: $\sigma^{(0+1)}$; upper solid: $\sigma^{(0+1+2)}$. The dashed curve represents the exact next-to-leading order calculation for $t\bar{t}$ production, in excellent agreement with $\sigma^{(0+1)}$. The dotted curve is our resummed prediction.
• Figure 2: Optimum number of perturbative terms in the exponent with PVR. The solid family is for PVR and the dashed set for the perturbative approximation, both families increasing, for parametric values $n=10,20,30,40$.
• Figure 3: Differential cross sections $d\sigma/d\eta$ for $p \bar{p} \rightarrow t \bar{t} X$ at $\sqrt{S}=1.8$ TeV and $m =$175 GeV in the $\overline{\rm MS}$-scheme for (a) the $q\bar{q}$ and (b) the $gg$ channel: Born (dotted), next-to-leading order (dashed), and resummed (solid).
• Figure 4: Inclusive cross section for heavy quark production at $\sqrt{S}=$ 1.8 TeV in the $\overline{\rm MS}$ scheme. The dashed curves show our perturbative uncertainty band, while the solid curve is our central prediction.
• Figure 5: Renormalization/factorization hard scale dependence of the resummed (solid) and next-to-leading order (dashed) cross sections at $\sqrt{S}=$ 1.8 TeV for $m =$175 GeV.