The chiral symmetry of domain wall fermions makes the calculation of the nucleon axial charge particularly easy since the Ward-Takahashi identity requires the vector and axial-vector currents to have the same renormalization, up to lattice spacing errors of order O(a~2). The DBW2 gauge action provides enhancement of the good chiral symmetry properties of domain wall fermions at larger lattice spacing than the conventional Wilson gauge action. Taking advantage of these methods and performing a high statistics simulation, we find a significant finite volume effect between the nucleon axial charges calculated on lattices with (1.2 fm)~3 and (2.4 fm)~3 volumes (a ≈ 0.15 fm). On the large volume we find gA = 1.212 ± 0.027(stat) ± 0.024(norm). The quoted systematic error is the dominant one, corresponding to current renormalization. This theoretical first principles calculation, which does not yet include isospin breaking effects, yields a value of gA only a little bit below the experimental one, 1.2670 ± 0.0030.
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