Aspects of Quantum Chromodynamics *

These lectures provide an overview of Quantum Chromodynamics (QCD), the SU (3) C gauge theory of the strong interactions. The running of the strong coupling and the associated property of Asymptotic Freedom are analyzed. Some selected experimental tests and the present knowledge of αs and the quark masses are briefly summarized. A short description of the QCD flavour symmetries and the dynamical breaking of chiral symmetry is also given. A more detailed discussion can be found in standard textbooks 1,2,3,4 and recent reviews 5,6. A fast look into the Particle Data Tables 7 reveals the richness and variety of the hadronic spectrum. The large number of known mesonic and baryonic states clearly signals the existence of a deeper level of elementary constituents of matter: quarks 8. In fact, the messy hadronic world can be easily understood in terms of a few constituent spin-1 2 quark flavours: Q = + 2 3 u c t Q = − 1 3 d s b Assuming that mesons are M ≡ q ¯ q states, while baryons have three quark constituents, B ≡ qqq, one can nicely classify the entire hadronic spectrum. There is a one–to–one correspondence between the observed hadrons and the states predicted by this simple classification. Thus, the Quark Model appears to be a very useful Periodic Table of Hadrons. However, the quark picture faces a problem concerning the Fermi–Dirac statistics of the constituents. Since the fundamental state of a composite system is expected to have L = 0, the ∆ ++ baryon (J = 3 2) with J 3 = + 3 2 corresponds to u ↑ u ↑ u ↑ , with the three quark spins aligned into the same direction (s 3 = + 1 2) and all relative angular momenta equal to zero. The wave function is symmetric and, therefore, the ∆ ++ state obeys the wrong statistics. The problem can be solved assuming 9 the existence of a new quantum number, colour, such that each species of quark may have N C = 3 different