Using the replica method, we analyze the mass dependence of the QCD 3 partition function in a parameter range where the leading contribution is from the zero momentum Goldstone fields. Three complementary approaches are considered in this article. First, we derive exact relations between the QCD 3 partition function and the QCD 4 partition function continued to half-integer topological charge. ...

Quantum Chromodynamics (QCD) is the theory governing the strong interaction of particles. It describes the interactions that bind quarks and gluons into protons and neutrons, and binds these into nuclei. We believe QCD to be as fundamental and complete as QED, the theory of electromagnetic interactions, whose predictions have been tested to more than ten decimal places. If it were possible to m...

We compute the mass of the charm quark using both quenched and dynamical lattice QCD calculations. We examine the effects of mass dependent lattice artifacts by comparing two different formalisms for the heavy quarks. We take the continuum limit of the charm mass in quenched QCD by extrapolating from three different lattice spacings. At a fixed lattice spacing, the mass of the charm quark is co...

Quantum Chromodynamics (QCD) provides an excellent description of nature; however, the theory suffers from divergences that must be removed to render it finite. Lattice QCD provides an apriori non-perturbative regularization of QCD that makes it amenable to analytic and computational methods. No model assumptions other than QCD itself are needed to formulate the theory. This review surveys the ...

After a brief historical review of the emergence of QCD as the quantum field theory of strong interactions, the basic notions of colour and gauge invariance are introduced leading to the QCD Lagrangian. The second lecture is devoted to perturbative QCD, from tree-level processes to higher-order corrections in renormalized perturbation theory, including jet production in e + e − annihilation , h...

In 1973, with the discovery of asymptotic freedom , QCD was at the frontier of particle physics studies. Now, in 2006, QCD is strongly installed (returning) at the center of particle physics researches. This, not only because of the abundance of data on jet emission at HERA and Tevatron, but especially for the necessity of preparing tools for discoveries at LHC. Indeed, events with large ET , a...

We study the phase diagrams of N = ∞ vector-like, asymptotically free gauge theories as a function of volume, on S3 × S1. The theories of interest are the ones with fermions in two index representations [adjoint, (anti)symmetric, and bifundamental abbreviated as QCD(adj), QCD(AS/S) and QCD(BF)], and are interrelated via orbifold or orientifold projections. The phase diagrams reveal interesting ...