Quark statistics and baryon form factors

Abstract

Using the Gell-Mann-Zweig triplet model of quarks (Q), it is shown that the orbital structure of the 3Q wave function has a strong influence on the shape of the baryon form factors. In particular, an antisymmetric wave function (A) predicts nodal behavior of the proton charge form factor even at values of q²∼20 F⁻², in complete disagreement with observation. On the other hand, a symmetrical wave function (S) not only leads to a smooth structure for this quantity, but shows a pattern in qualitative agreement with experiment. Such a wide difference in predictions is physically due to the fact that while an S function of L=0 can be easily formed with the basic clusters (1,1) and (2,1) in S-wave pairs, an A function of L=0 needs at least unit values of the partial angular momenta associated with the above clusters. The implication of this result is that within the 56 representation of SU₆, it discriminates against Fermi statistics which requires A-type functions to go with 56, and favors a sort of parastatistics which at least allows S-type functions in 56. The validity of this "selection rule" is strictly within the premises of a single-triplet quark model, and does not rule out other possibilities in the context of more extended quark models.