Baryons, quark structure

The weak interactions change quark and lepton flavors, e.g., a d-quark into -quark or a muon into an electron (this latter, e.g., in the p e Vet /i process). The quark structures of the proton and neutron as well as the properties of nucleons are presented in O Table 2.3. The baryons are built up from three (valence) quarks and massless gluons, but they contain also dynamical (or sea) quarks (quark-antiquark pairs) in a small quantity. The mesons are built up from quark-antiquark pairs and gluons. 

As a first step in this direction we will discuss here the two flavor color superconducting (2SC) quark matter phase which occurs at lower baryon densities than the color-flavor-locking (CFL) one, see [18, 32], Studies of three-flavor quark models have revealed a very rich phase structure (see [32] and references therein). However, for applications to compact stars the omission of the strange quark flavor within the class of nonlocal chiral quark models considered here may be justified by the fact that central chemical potentials in stable star configurations do barely reach the threshold value at which the mass gap for strange quarks breaks down and they appear in the system [20], Therefore we will not discuss here first applications to calculate compact star configurations with color superconducting quark matter phases that have employed non-dynamical quark models... 

However a simple, mnemonic rule emerges each mesonic (baryonic) state has the quantum number content of an appropriate quark-antiquark (three quark) system. The structure of mesons and baryons in terms of quarks and antiquarks is outlined below and the reader is referred for details to Lichtenberg (1978). 

A large part of the present experimental activity concerns baryons with heavy flavours, Qqq or Qqs or Qss, where q means u or d. These states, with their helium-like structure, are much more asymmetric the two light quarks are rotating rather fast around a flavoured quark which remains almost static. In the near future, double-charm baryons QQq should provide interesting information on quark dynamics with the superposition, within the same hadron, of the slow motion of two heavy quarks experiencing the short-range QCD potential, and of the fast motion of a light quark around them [7,8]. 

Isospin wave functions are built in exactly the same way, with f replaced by u and i replaced by d. States with three identical quarks such as those of the ft family (sss) have a simple structure either the spin wave function corresponds to spin 5 = 3/2 and the space wave function has to be symmetric, or the total spin is 5 = 1/2 and one should combine the corresponding spin wave functions with a pair of mixed-symmetry space wave functions, as in eq. (3.33), to form an overall spin-space wave function which is symmetric. The above combinations are also found in qqq baryons made of ordinary quarks (q = u or d), when isospin is 7 = 3/2. This is the A family. When isospin is 7 = 1 /2, i.e., for the nucleon family, new arrangements exist. First, isospin 7 = 1/2 and spin 5 = 1/2 can be combined to form a symmetric spin-isospin wave function. This is what occurs for the nucleon itself and some of its excitations. The spin-isospin wave function can also be of mixed symmetry and is associated with a mixed-symmetry spatial wave function. Finally, there is the possibility of an antisymmetric spin-isospin wave function which allows for the use of an antisymmetric spatial wave function such as p x Aexp[-a(p + A )j. 

Diquarks are almost as old as quarks. The possibility that quarks might cluster pairwise in baryons, leading to a simple two-body structure, has been suggested by many authors since the early days of the quark model. There are currently many speculations on the use of diquarks to analyse baryon production in e e" experiments, in hadronization of jets, or in the decay of heavy particles [11]. We shall restrict ourselves here to the domain of baryon spectroscopy. 

This suggests analysing rigorously to what extent diquark clustering actually results from the quark dynamics. For instance, it was claimed for many years that orbitally excited baryons should consist of a quark and a diquark at both ends of a rotating string, with a colour (3-3) structure, since the... 

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