The Theory of Quark and Gluon Interactions
F. J. Ynduráin's book on Quantum Chromodynamics has become a classic among advanced textbooks. First published in 1983, and translated into Russian in 1986, it now sees its fourth edition. It addresses readers with basic knowledge of field theory and part
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r, 546 b.c.e.
1.1 The Rationale for QCD
Historically, quantum chromodynamics (QCD) originated as a development of the quark model. In the early sixties it was established that hadrons could be classified according to the representations of what today we would call flavour SUF (3) (Gell-Mann, 1961; Ne’eman, 1961). This classification presented a number of features that are worth noting. First of all, only a few, very specific representations occurred; they were such that they built representations of a group SU (6) (G¨ ursey and Radicati, 1964; Pais, 1964) obtained by adjoining the group of spin rotations SU (2) to the internal symmetry group, SUF (3). However, neither for SUF (3), or SU (6) did the fundamental representations (3 and ¯ 3 for SUF (3)) appear to be realized in nature. This led Gell-Mann (1964a) and Zweig (1964) to postulate that physical hadrons are composite objects, made up of three quarks (baryons) or a quark-antiquark pair (mesons). These three quarks are now widely known as the three flavours, u (up), d (down) and s (strange); the first two carry the quantum numbers of isospin, and the third strangeness. It has been found that precisely those representations of SUF (3) occur that may be obtained by reducing the products 3 × 3 × 3 (baryons) or 3 × ¯ 3 (mesons); when the spin 1/2 of the quarks is taken into account, the SU (6) scheme is obtained. In addition, the mass differences of the hadrons may be understood by assuming md − mu ≈ 4 MeV,
ms − md ≈ 150 MeV,
(1.1.1)
together with eventual electromagnetic radiative corrections. The electric charges of the quarks, in units of the proton charge, are Qu = 23 ,
Qd = Qs = − 13 .
(1.1.2)
That hadrons are composite objects was a welcome hypothesis on other grounds, too. For example, it is known that the magnetic moment of the h/2mp , instead of the value µp = e¯h/2mp expected if proton is µp = 2.79 × e¯ it were elementary. The values of the magnetic moments calculated with the
2
Chapter 1
quark model (first developed by Morpurgo and by Dalitz and collaborators) are, on the other hand, in reasonable agreement with experimental results. These successes stimulated a massive search for quarks that still goes on. None of the candidates found to this date has been confirmed, but at least we have a lower bound (of the order of 200 GeV) for the mass of free quarks, which seemed to imply that hadrons are very tightly bound states of quarks indeed. This picture, however, can be challenged on at least two grounds. First, the fundamental state of a composite system, in the SU (6) scheme, is one in which all relative angular momenta vanish. Thus the ∆++ resonance had to be interpreted as being made up of u ↑ , u↑ , u↑ ,
(1.1.3)
(where the arrows stand for spin components) at relative rest. However, this is preposterous: being spin one-half objects, quarks should obey Fermi–Dirac statistics and their states should be antisymmetric, which is certainly not the case in (1.1.3). Second, one can use current algebra techniques (GellMann, Oakes and Renner, 1968; Glashow an
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