Properties of axial-vector-current divergences in the constituent-quark basis

Abstract

The properties of the axial-vector currents and their divergences are examined in the context of the quark model as quantized on the null plane. The SU(3) transformation properties of the divergences are not as they naively appear to be. It is found that correction terms to strong PCAC (partial conservation of axial-vector current) are expected, especially for kaons, and that these terms are likely to be proportional to one-body quark operators (and therefore octet operators), but that the proportionality constants may have a mixture of linear and quadratic dependence on the quark mass parameters. In view of this, some consequences of the one-body nature of the PCAC-correction terms are derived without making any assumptions of SU(3) algebraic structure. A universality relation which was recently obtained by Dominquez is a direct result of this line of reasoning; furthermore, assuming the pion PCAC correction ${\Delta }_{\pi }$ is small, a value for ${\Delta }_K$ of approximately 0.2 follows. This then is used to correct some old PCAC formulas, bringing them into agreement with experiment. Finally, the consequences of some assumptions concerning the SU(3) properties of the axial divergences are explored.