Delocalization of the axial charge in the chiral limit

The nucleon's axial vector charge, g_A, becomes delocalized in the chiral limit. When m_\pi = 0, and SU(2)_L x SU(2)_R is exact, 1/3 of the nucleon's axial charge is to be found at infinite distance from the nucleon. For finite m_\pi this result is approached smoothly as m_\pi -> 0. We illustrate this effect by considering the lepton-proton spin-spin interaction arising from Z^0 exchange as a function of m_\pi. Delocalization may have implications for lattice calculations of g_A and in nuclei.