Abstract
As stated at the very beginning of this text, the first evidence in the direction of QCD came from the quark model of hadrons; that is to say, from the fact that hadrons can be classified as colour singlet bound states ̄;q′;, qq′q″. These states, including radial and angular excitations, do indeed accommodate the vast majority of the hundreds of hadrons known today (see the Particle Data Group tables). There are only a few dubious cases, and two or three hadrons that can be interpreted as being made mostly of gluons, called glueballs. Not only this, but some of the quantitative properties of these hadrons, in particular mass differences, were roughly understood in simple potential models well before the advent of QCD. In the present chapter we will review the situation, of course (whenever possible) within the context of the fullfledged theory of quark and gluon interactions. From this point of view, it is convenient to split the subject into three broad areas.
“You boil it in sawdust: you salt it in glue: You condense it with locusts and tape: Still keeping one principal object in view — To preserve its symmetrical shape”
Lewis Carroll, 1897
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References
See, for example, the reviews of Lepage and Thacker (1988) and Grinstein (1991) .
We neglect spin for the time being.
See, e.g., Bjorken and Drell (1965), Sect. 15.2.
See e.g., Gupta and Radford (1981); Brambilla, Consoli and Prosperi (1994) .
See standard textbooks on relativistic quantum mechanics: Akhiezer and Berestetskii (1963); Berestetskii, Lifshitz and Pitaevskii (1971); Ynduráin (1996) .
The Fourier transforms of the various terms may be easily evaluated with the help of the table in the appendix of Titard and Ynduráin (1994) .
We will show this later in an explicit calculation of the diagram where both nonperturbative gluons are attached to the exchanged one. A more rigorous discussion will be presented in Sect. 6.4, following the methods of Dosch and Simonov.
With correction for one case by Pineda (1997a) .
Dosch (1987); Simonov (1988, 1989b); Dosch and Simonov (1988); Bertmann, Dosch and Krämer (1989) . See also Simonov, Titard and Ynduráin (1995) .
By “Lagrangians” we mean here the integrated Lagrangian densities.
In actual quarkonium states, none of the regimes to be described is fully operative; the first regime would be certainly applicable with very good approximation only for toponium with n up to n= 4.
Our derivation of these formulas is not rigorous. A rigorous derivation would require to make the calculations in Euclidean QCD, to be described in detail in Sects. 9.1 ff, and go back to Minkowski space at the end.
Buchmüller (1982) . See also Eichten and Feinberg (1981) and Brambilla, Consoli and Prosperi (1994) for more refined derivations.
Chodos et al. (1974); Chodos, Jaffe, Johnson and Thorn (1974) . See Hasenfratz and Kuti (1978), Johnson (1975) and Alvarez-Estrada et al. (1988) for reviews.
More details of this solution may be found in stand rd textbooks: Akhiezer and Berestetskii (1963); Greiner, Müller and Rafelski (1 85); Ynduráin (1996) .
It has been proposed to at least partially repair this by introducing an independent pion field, defined to be zero inside the bag, and an elementary pseudoscalar field outside; this is the so-called “little bag”, which has enjoyed some success, particularly in the realm of nuclear physics. We refer the reader to the original papers: Brown, Rho and Vento (1979); Vento et al., (1980).
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Ynduráin, F.J. (1999). Hadrons as Bound States of Quarks. In: The Theory of Quark and Gluon Interactions. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03932-8_6
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DOI: https://doi.org/10.1007/978-3-662-03932-8_6
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