We have recently examined the static properties of the baryon octet (magnetic moments and axial vector coupling constants) in a generalized quark model in which the angular momentum of a polarized nucleon is partly spin $〈S_z〉$ and partly orbital $〈L_z〉.$ The orbital momentum was represented by the rotation of a flux tube connecting the three constituent quarks. The best fit is obtained with $〈S_z〉=0.08\mathrm{}\pm 0.15$, $〈L_z〉=0.42\mathrm{}\pm \mathrm{0.14.}$ We now consider the consequences of this idea for the $q^2$ dependence of the magnetic and axial vector form factors. It is found that the isovector magnetic form factor $G_M^{\mathrm{isovec}}{(q}^2)$ differs in shape from the axial form factor $F_A{(q}^2)$ by an amount that depends on the spatial distribution of orbital angular momentum. The model of a rigidly rotating flux tube leads to a relation between the magnetic, axial vector and matter radii, $〈r^2{〉}_{\mathrm{mag}}{=f}_{\mathrm{spin}}〈r^2{〉}_{\mathrm{axial}}+\frac{5}{2}{f}_{\mathrm{orb}}〈r^2{〉}_{\mathrm{matt}},$ where $f_{\mathrm{orb}}{/f}_{\mathrm{spin}}=\frac{1}{3}〈L_z〉{/G}_A,$ $f_{\mathrm{spin}}{+f}_{\mathrm{orb}}=1.\mathrm{}$ The shape of $F_A{(q}^2)$ is found to be close to a dipole with $M_A=0.92\mathrm{}\pm 0.06$ GeV.

• Received 16 March 1998

DOI:https://doi.org/10.1103/PhysRevD.58.033002