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Can the nucleon axial charge be O(Nc^0)?

The nucleon self-energy and its relation to the nucleon axial charge gA are discussed at large Nc. The energy is compared for the hedgehog, conventional, and recently proposed dichotomous nucleon wavefunctions which give different values for gA. We consider their energies at both perturbative and non-perturbative levels. In perturbative estimates, we take into account the pion exchanges among quarks up to the third orders of axial charge vertices, including the many-body forces such as the Wess-Zumino terms. It turns out that the perturbative pion exchanges among valence quarks give the same leading Nc contributions for three wavefunctions, while their mass differences are O(Lamba_qcd). The signs of splittings flip for different orders of the axial charge vertices, so it is hard to conclude which one is the most energetically favored. For non-perturbative estimates involving the modification of quark bases, we use the chiral quark soliton model as an illustration. With the hedgehog quark wavefunctions with gA of O(Nc), we investigate whether solutions with coherent pions are energetically favored. Again it is hard to give decisive conclusions, but it is likely that adding the confining effects disfavors the solution with the coherent pions, making a pion cloud around a nucleon quantum rather than coherent. The nuclear matter at large Nc is also discussed in light of the value of gA.