New QCD Sum Rules for Nucleon Axial Vector Coupling Constants

New QCD sum rules for the nucleon axial-vector current coupling constants are derived. One set is derived from a generalized correlator of spin-1/2 interpolating fields, and the other with a mixed correlator of spin-1/2 and spin-3/2 fields. Using a recently-developed Monte-Carlo based uncertainty analysis and techniques for determining the optimal interpolating fields, the predicative ability of QCD sum rules for axial-vector current coupling constants are determined. We find the previous studies of this matrix element are based on an invalid sum rule. A combined analysis of this sum rule together with the nucleon mass sum rules yields $g_A=1.48\pm^{1.06}_{0.65}$. The relative error of approximately 60% is large compared to a 10% error for the nucleon mass obtained from the same input parameters.