Dressed quarks and the nucleon's axial charge

The nucleon's axial charge, g(A), expresses features that are both fundamental to the strong interaction and crucial to its connection with weak-interaction physics. We show that dynamical chiral symmetry breaking (DCSB) suppresses the axial charge of a dressed quark, g(A)(q), at infrared momenta. Since this effect disappears as chiral symmetry is restored, one may argue that g(A) vanishes with the restoration of chiral symmetry because no nucleon bound state survives the associated transition. The suppression of g(A)(q) is shown to be part of an explanation for a 25% reduction of g(A) from its nonrelativistic quark-model value. Critical, too, however, is the presence of dressed-quark angular momentum within the nucleon. The value of g(A)(q) depends on the kernels of the gap and Bethe-Salpeter equations. We find that incorporation of essentially nonperturbative effects associated with DCSB into these kernels inflates the value relative to that obtained at leading order in a widely used truncation of QCD's Dyson-Schwinger equations. Such corrections also affect the nucleon's axial radius. In both cases, however, agreement with experiment will require similar improvements to the Faddeev kernel and associated interaction current.