Chapter 1 Two Quark Potentials

In this Chapter QCD interactions between a quark and an anti-quark are discussed. In the heavy quark limit these potentials can be related to quarkonia and 1/m corrections can be systematically determined. Ex-citations of the ground state potential provide an entry point into the phenomenology of quark-gluon hybrids. The short-distance behaviour of non-perturbative potentials can serve as a test of resummation and convergence of perturbative expansions. Torelons and potentials between non-fundamental colour charges offer a window into the origin of the confinement mechanism and relate to effective string descriptions of low energy aspects of QCD. 1.1 Motivation In order to avoid excessive overlap with the many introductions that already exist in different places of this Volume, we shall elaborate on a very subjective motivation of studying interquark potentials in QCD, centred around the general theme of building bridges between models and QCD. QCD contains two related, non-perturbative features: the breaking of (approximate) chiral symmetry and the (effective) confinement of coloured objects such as quarks and gluons. Similarly, models of the QCD vacuum can roughly be divided into two classes: those that are primarily based on chiral symmetry and those that have confinement, for instance in the form of a confining potential, as their starting point. Often it is difficult to microscopically relate a particular model to QCD. For example, should the instantons that are evidenced in lattice simulations within a given pre