Hadronic Physics from Lattice QCD

The following sections are included:

• Preface

• Contents

I review the results of hadron spectroscopy calculations from lattice Quantum Chromodynamics (QCD) for an intended audience of low energy hadronic physicists. I briefly introduce the ideas of numerical lattice QCD. The various systematic errors, such as the lattice spacing and volume dependence, in lattice QCD calculations are discussed. In addition to the discussion of the properties of ground state hadrons, I also review the small amount of work done on the spectroscopy of excited hadrons and the effect of electromagnetic fields on hadron masses. I also discuss the attempts to understand the physical mechanisms behind hadron mass splittings.

We review lattice QCD results for glueballs (including a discussion of mixing with scalar mesons), hybrid mesons and other exotic states (such as B_sB_s molecules).

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. Excitations 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.

The effective residual interaction for a system of hadrons has a long tradition in theoretical physics. It has been mostly addressed in terms of boson exchange models. The aim of this review is to describe approaches based on lattice field theory and numerical simulation. At the present time this subject matter is in an exploratory stage. A large array of problems waits to be tackled, so that known features of hadron-hadron interactions will eventually be understood in a model-independent way. The lattice formulation, being capable of dealing with the nonperturbative regime, describes strong-interaction physics from first principles, i.e. quantum chromodynamics (QCD). Although the physics of hadronhadron interactions may be intrinsically complicated, the methods used in lattice simulations are simple: For the most part they are based on standard mass calculations. This chapter addresses commonly used techniques, within QCD₃₊₁ and also simpler lattice models, describes important results, and also gives some insight into numerical methods for multi-quark systems.

A review is given of attempts to bridge the gap between everyday particle and nuclear physics — involving many quarks — and the basic underlying theory of QCD that can only be evaluated exactly for few quark systems. Even the latter requires the original theory of QCD to be discretised to give Lattice QCD — but this modification can still yield exact results for the original theory. These LQCD results can then be considered on a similar footing to experimental data — namely as cornerstones that must be fitted by phenomenological models. In this way, the hope is that “QCD inspired” models can become more and more “QCD based” models, by fixing — in the few-quark case where LQCD can be carried out — the form of these models in such a way that they can be extended to multi-quark systems.