QCD resummation and heavy quark cross sections

TL;DR

The work tackles the challenge of predicting heavy-quark production in high-energy hadron collisions by combining fixed-order perturbative QCD with all-order soft-gluon resummation of threshold logarithms. It systematically develops and applies a formalism that accounts for color exchange in the hard scattering, enabling next-to-leading logarithmic resummation and its extension beyond Drell-Yan to heavy-quark production via qqbar and gg channels. The study provides detailed results for top production at the Tevatron and bottom production at HERA-B, including cross sections and differential distributions (pT and rapidity), highlighting the dominant threshold-region contributions and the dependence on factorization schemes and scales. The generalized resummation framework, together with explicit anomalous-dimension matrices for key partonic processes, enhances the reliability of QCD predictions and offers a path toward more precise phenomenology in heavy-quark production and related hard-scattering observables.

Abstract

In this dissertation a detailed analysis of heavy quark production is given with an emphasis on the resummation of soft gluon corrections. First we calculate the production cross sections for top quark production at the Fermilab Tevatron and for bottom quark production at fixed-target $pp$ experiments, and in particular HERA-B. We consider both the order $α_s^3$ cross sections and the resummation of soft gluon corrections in all orders of QCD perturbation theory. Then we calculate the inclusive transverse momentum and rapidity distributions for top quark production at the Fermilab Tevatron and bottom quark production at HERA-B. We give both $α_s^3$ and resummed results. Finally, we discuss the resummation of distributions that are singular at the elastic limit of partonic phase space (partonic threshold) in QCD hard-scattering cross sections, such as heavy quark production. We show how nonleading soft logarithms exponentiate in a manner that depends on the color structure within the underlying hard scattering. This result generalizes the resummation of threshold singularities for the Drell-Yan process, in which the hard scattering proceeds through color-singlet annihilation. We illustrate our results for the case of heavy quark production by light quark annihilation and gluon fusion, and also for light quark production through gluon fusion.

Figures (43)

• Figure 1.1: The strong coupling constant $\alpha_s$ versus scale
• Figure 2.2: The scaling functions $f_{q\bar{q}}^{(k,0)}$ in the $\overline {\rm MS}$ scheme. Plotted are $f_{q\bar{q}}^{(0,0)}$ (exact, upper solid line at large $\eta$; threshold approximation, upper dotted line at large $\eta$), $f_{q\bar{q}}^{(1,0)}$ (exact, lower solid line at large $\eta$; threshold approximation, lower dotted line at large $\eta$).
• Figure 2.3: Same as fig. 2.1 but now for the DIS scheme.
• Figure 2.4: Same as fig. 2.1 but now for $f_{gg}^{(k,0)}$ in the $\overline {\rm MS}$ scheme.
• Figure 2.5: The scaling functions $f_{q\bar{q}}^{(1,0)}$ in the $\overline {\rm MS}$ scheme. Plotted are the exact result (solid line), the leading S+V approximation (dotted line), the leading S+V approximation plus Coulomb terms (short-dashed line), the S+V approximation with leading plus subleading terms (long dashed line), and the S+V approximation with leading plus subleading terms plus Coulomb terms (dash-dotted line).