SU(6) strong breaking: structure functions and static properties of the nucleon

Abstract

In order to explain the experimental $x$ behavior of the ratio of deep-inelastic scattering structure functions $\frac{F_2^{\mathrm{en}}}{F_2^{\mathrm{ep}}}$, which is a manifestation of SU(6) breaking, we propose to introduce, in the harmonic-oscillator quark model, the following interband mixing for the nucleon wave function at rest: $cos\varphi {(56,0^{+})}_{N=0\mathrm{}}+sin\varphi {(70,0^{+})}_{N=1\mathrm{}}$. The effect on the $x$ behavior of the ratio $\frac{F_2^{\mathrm{en}}}{F_2^{\mathrm{ep}}}$ is linear in $tan\varphi$, the angle is found to be $\varphi \simeq -20\mathrm{}°$. It turns out that the famous successes of unbroken SU(6) for the low-lying-octet static properties are not broken significantly, $\frac{{\mu }_p^{\mathrm{tot}}}{{\mu }_n^{\mathrm{tot}}}\simeq -\frac{3}{2}\mathrm{}(1+0.03)\mathrm{}$, ${\left(\frac{F}{D}\right)}_{\mathrm{axial}-\mathrm{vector}}\simeq \frac{2}{3}\mathrm{}(1+0.02)\mathrm{}$, since the breaking effect is proportional to ${tan}^2\varphi$ with reducing coefficients. Moreover, the mixing implies a slope for the neutron electric form factor, which is a linear effect in $tan\varphi$, of the right sign and order of magnitude. $\left|\frac{G_A}{G_V}\right|$ is correctly predicted to be 1.25. The chiral configuration mixing describing the nucleon wave function at $P_z=\infty$ is shown to come from the combination of two effects: (i) introduction of small components in the quark Dirac spinors to account for the highly relativistic internal quark velocities as described in our previous papers, which preserves the 56 assignment of the nucleon wave function at rest, and (ii) the new effect of SU(6) mixing for the nucleon wave function at rest. Introducting a structure for the quarks which parallels the need for quark structure in the leptoproduction of hadrons, we end with a good description of the unpolarized structure functions in deep-inelastic electro- and neutrino-production. Further predictions are made of the yet-unmeasured asymmeties in deep-inelastic polarized electroproduction. Careful comparison is made with previous works by Altarelli et al. and Close, who have adopted different approaches.