The quark statistics

The lowest lying states, in the naive quark model (Gell-Mann, 1964 Zweig, 1964) of the most common baryons, consist of triplets (qqq) of u,d and s quarks in relative s-wave configurations, since if the kinetic energy is to be a minimum the space wave function cannot have nodes and must be symmetric. Phenomenologically, in order to agree with the spectra of known particles, one finds that the spin and isospin parts must also be symmetric. Thus we have totally symmetric wave functions in violation of the Pauli principle if quarks are fermions as they have to be. 

The classic example is the N resonance A(1238) with spin and isospin It thus requires all quark spins and isospins pointing in the same direction, and is completely symmetric, e.g. u u u where 

At a more sophisticated level, if one tries to incorporate ordinary spin with the usual SU (3) one is led to the celebrated SU(6) symmetry group (Gursey and Radicati, 1964 Sakita, 1964) (in analogy to what is done in nuclear physics where one combines SU 2) for spin with the 517(2) for isospin to get 517(4)), where the quarks form a representation, the 6, with components 

Of these the 56 is totally symmetric whereas the 20 is totally antisymmetric. 

According to the generalized Pauli principle, one expects the complete wave function of the baryon to be antisymmetric, and since the ground state baryon 517(6) supermultiplet is a symmetric s-state, the favoured SU(6) representation ought to be the 20, whose content in terms of flavour and ordinary spin is 

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