50 Years of quantum chromodynamics
Abstract
Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution . It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant, $$\alpha _s(Q^2)$$ α s ( Q 2 ) , that varies with the energy scale $$Q^2$$ Q 2 characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of $$\alpha _s$$ α s at low momentum transfers limits perturbative calculations to the high-energy region where $$Q^2\gg \varLambda _{{\textrm{QCD}}} ^2\simeq $$ Q 2 ≫ Λ QCD 2 ≃ (250 MeV) $$^2$$ 2 . Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD…
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