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 $q^2\sim 20 {\mathrm{F}}^{-2\mathrm{}}$, 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 $L=0\mathrm{}$ can be easily formed with the basic clusters (1,1) and (2,1) in $S$-wave pairs, an $A$ function of $L=0\mathrm{}$ 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 $S{U}_6$, 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.