On the transformation between current and constituent quarks and consequences for polarised electroproduction structure functions

Abstract

The transformation of Buccella et al. and of Melosh is a rotation in spin space, so spin-dependent matrix elements are sensitive to this transformation, while spin-averaged quantities are not. This is explicitly shown by applying this transformation to the nucleon constituent space SU(6) wave function and the generated current space wave function is seen to be simply a spin rotation of the constituent state. Matrix elements of current operators are then calculated with special emphasis on polarised electroproduction where the results of Kuti and Weisskopf, which ignored this transformation, are vitiated. It is shown that the current quarks generated by this transformation cannot be identified with quark partons and the properties of a more general operator which is a candidate for such a transformation are discussed. The nucleon octet states are decomposed into SU(6) parton configurations and elastic and inelastic matrix elements within the octet are computed. The following sum rule is derived for the asymmetry in polarised electroproduction on polarised protons ∫ 0 1 dx G 1 γ p (x) ≅ 1 3 gA gV , and the relation with previous sum rules is clarified. In the limit x → 1 we predict that the polarisation asymmetries from proton and neutron will be equal.