A model for the $Q^2$ dependence of polarized structure functions

Abstract

We present an update of a phenomenological model for the spin dependent structure functions $g_1(x,Q^2)$ of the proton and neutron. This model is based on a broken SU(6) wavefunction parametrized by the unpolarized structure functions. The two free parameters of the model are choosen to fulfill the Bjorken and Ellis--Jaffe sum rules. The model respects isospin symmetry and has zero strange sea polarization. Using new values for $F/D$ from hyperon beta decay the resulting $Q^2$ dependent asymmetries $A_1$ are in perfect agreement with the existing data. Therefore we do not see any evidence for a ``spin crisis''. With two choices for $g_2$ the $Q^2$ dependence of $A_1(x,Q^2)$ and $A_2(x,Q^2)\sqrt{Q^2}/M$ is predicted and shown to be small for both cases.