Chiral configuration mixing and deep-inelastic scattering of polarized leptons by polarized nucleons

Abstract

In the quark model, a large SU(3) \ensuremath{\bigotimes} SU(3) configuration mixing appears at ${P}_{z}=\ensuremath{\infty}$ as a relativistic effect due to the high internal velocities for quarks inside hadrons. This mixing describes the relative alignment between the nucleon helicity and the helicities of the quarks. Since the quark-parton model is understood in a frame where the nucleon has a large momentum, we propose to take into account this large mixing in the calculation of the spin-dependent effects in deep-inelastic scattering of a polarized lepton (electron or muon) by a polarized nucleon. The scaling of the spatial wave function is ensured by the Lorentz contraction. Unlike a previous quark-parton model calculation by Gourdin, we take into account the configuration mixing in the estimation of the singlet contribution to the asymmetries. We express our results in terms of the SU(3) \ensuremath{\bigotimes} SU(3) mixing parameters. Assuming that the nucleon is a superposition of irreducible SU(3) \ensuremath{\bigotimes} SU(3) representations allowed by the quark model, we can express the singlet contribution in terms of the $F$, $D$ couplings of the low-lying octet axial-vector matrix elements. The neutron asymmetry appears to be proportional to the deviation of $\frac{F}{D}$ from the SU(6) value $\frac{2}{3}$. As expected, the Bjorken sum rule for the difference between the proton and neutron asymmetries is satisfied. In our specific model, where the spin part of the wave function at rest is expressed in terms of free Dirac spinors, we have $\frac{F}{D}=\frac{2}{3}$, so that we predict a large positive proton asymmetry and a null asymmetry for the neutron, ${A}^{p}=\frac{1}{3}|\frac{{G}_{A}}{{G}_{V}}|$, ${A}^{n}=0$.