1.2 Old, present, and future baryon spectroscopy

The successful picture of the baryon spectrum was one of the most striking of the early achievements of the quark model and its precursors based on unitary symmetries [3]. Everyone remembers the prediction of the Ω⁻ particle, the strangeness S = −3 member of the decuplet of J^P = (3∕2)⁺ baryons. Simple formulae relate the masses of ground-state baryons of increasing strangeness. We shall come back to their microscopic grounds in Chapters 8 and 11. Besides this

horizontal scanning of the mass spectrum, the excitation patterns i.e., the

vertical aspects of the spectrum were quite well described in terms of the harmonic-oscillator model [4]. More meson nucleon resonances have been identified meanwhile [5], all fitting quite well into the picture of the three-quark model with spin, radial, or orbital excitations [6]. These

early baryons approximately obey SU(3)_F flavour symmetry: the wave function, including colour, spin, space, and flavour degrees of freedom, is antisymmetric under the exchange of any pair of quarks. The changes induced by the mass difference between the d and the u quarks or between the ordinary and the strange quarks can be treated as small corrections.

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]. With triple-charm baryons, we will recover an exact antisymmetry of the wave function. The ccc baryons will exhibit an interesting spectrum of narrow levels [9, 10]. In quarkonium spectroscopy, excitations become broad only when they lie above the Zweig-allowed threshold QQ → Qq + qQ . Likewise, triple-charm baryons are narrow until one reaches the threshold for flavour splitting: QQQ → QQq + q Q. The first excitations, which lie below this threshold, will be stable under strong interactions, with only electromagnetic decay QQQ^∗ → QQQ + γ. Of course, each unit of charm added to a baryon implies a great suppression factor in the production rate and, a more dramatic effect, an increase of the eventual multiplicity of the decay and thus, by orders of magnitude, an increase in the difficulty of reconstructing the events. Although this is completely out of the scope of the present review, one may underline the fact that these flavoured baryons will provide extremely interesting information on weak interactions. The difference between the D⁺(cd ) and D^o(cu ) lifetimes tells us that, while decaying, the charm quark does not ignore its environment. To test the role of W exchange or annihilation or

penguin diagrams, it is crucial to measure the lifetimes and main branching ratios of the various species of charmed baryons [8].

In both charm and non-charm sectors, new problems have been raised in hadron spectroscopy. One question concerns the existence of localized

diquark clusters inside baryons [11]. Another hot topic concerns the possible

hybrid states qqqg with a valence gluon and, possibly, exotic quantum numbers. We find it important to analyse carefully the dynamics of

ordinary qqq baryons before concluding the need for new configurations.

We shall adopt here the naming scheme of the Particle Data Group. In the charm strange sector, we denote by Ξ_c a csq state of

Λ type, i.e., whose light-quark pair is mostly in a spin S = 0 state; Ξ_c^′ the csq state of spin 1 2 and of

Σ type, i.e., with the sq pair mostly in a spin S = 1 state; Ξ_c^∗ the spin 3 2 state. Double star will be given to any radial and orbital excitations. The ground state baryons made of ordinary, strange, or charmed quarks are listed in Table 1.1. The beauty analogues are easily extrapolated. The isospin wave functions will be given in Section 3.5.