Lattice QCD was invented thirty years ago but only in the last few years has it finally fulfilled its promise as a precision tool for calculations in hadron physics. This review will cover the fundamentals of discretising QCD onto a space-time lattice and how to reduce the errors associated with the discretisation. This ‘improvement’ is the key that has made the enormous computational task of a...

The hybrid quarkonium states are studied using the Born-Oppenheimer expansion. The first step in this expansion is the determination of the energy levels of the gluons in the presence of a static quark-antiquark pair as a function of the quark-antiquark separation. The spectrum of such gluonic excitations is determined from first principles using lattice QCD.

We present recent results on generalized parton distributions from dynamical lattice QCD calculations. Our set of twelve different combinations of couplings and quark masses allows for a preliminary study of the pion mass dependence of the transverse nucleon structure.

Lattice QCD is the only systematically improvable calculational tool we have for quantitatively understanding nonperturbative QCD effects. Accurate theoretical calculations of nonperturbative QCD effects are essential for the experimental flavor physics program. One set of goals of the experimental program are accurate determinations of the CKM matrix elements. This is illustrated for the weak ...

We review the status of lattice calculations of the deep-inelastic structure functions of the nucleon. In addition, we present some results on the pion and rho structure functions.

To reduce the size of this section's PostScript file, we have divided it into two PostScript files. We present the following index: PART 1 Page # Section name 1 9.1 The QCD Lagrangian 2 9.2 The QCD coupling and renormalization scheme 6 9.3 QCD in deep-inelastic scattering 9 9.4 QCD in decays of the τ lepton 11 9.5 QCD in high-energy hadron collisions PART 2

We perform the first studies of various inter-quark potentials in SU(3)c lattice QCD. From the accurate lattice calculation for more than 300 different patterns of three-quark (3Q) systems, we find that the static 3Q potential V3Q is well described by Y-Ansatz, i.e., the Coulomb plus Y-type linear potential. Quark confinement mechanism in baryons is also investigated in maximally-Abelian projec...

Motivated by the possible observation of the Θ+(1530), we study the quark structure of pentaquark states in quenched lattice QCD. The complete set of 19 local sources that have the proper symmetry for positive or negative parity isoscalar pentaquarks is constructed, as well as a nonlocal source composed of two displaced “good” diquarks. Quantitative structure information is determined from diag...

Lattice QCD results relevant to heavy quark physics are reviewed. In particular new results will be shown that, for the first time, include dynamical quarks in the QCD vacuum which are close enough to being realistic to allow accurate extrapolation to the physical point. Agreement with experiment is found for a wide range of spectral quantities and the implications of this for hadronic matrix e...

We briefly review the status of our understanding of hadron structure based on QCD. This includes the role of symmetries, especially chiral symmetry, and the insights provided by lattice QCD. The main focus is on baryon structure and especially the nucleon, but this cannot be treated realistically without reference to spectroscopy. Our aim is to highlight recent insights and promising direction...