Soft gluons and hard scales in QCD : Heavy quarks at finite and all orders

Abstract

The strong interaction of elementary particles is described by Quantum Chromodynamics (QCD). Utilizing this theory to describe and predict experimental data requires a number of concepts and techniques. Three of these, namely factorization, resummation and numerical phase space integration, are first reviewed and then applied here.

Factorization into perturbative and non-perturbative contributions is an essential tool in understanding scattering processes involving hadrons. After reviewing factorization in a general context the concept is particularized and applied to derive resummation. Observables in strong interactions are usually expressed as series in the strong coupling constant. Resummation allows one to derive all-order, albeit still perturbative information on such observables. It is explained in which way such resummation calculation are closely related, and indeed dependent on factorization. Deep-inelastic charm production is presented as a process into which valuable insights can be gained through resummation, taking into account also the polarizations of the initial state particles.

Whereas up to now resummation has been limited to those terms in the perturbation series kinematically dominant in some specific regions of phase space (e.g. near production thresholds), an extension of the method will be presented here to include also constant terms. In this context the discussion focusses on the Drell-Yan process.

Finally, numerical phase space integrations are investigated for a process involving the production of strongly interacting heavy final state particles. Here two methods, namely the phase space slicing and the dipole subtraction methods, are explained and compared as to their numerical performances.