Isospin Breaking in the Nucleon Isovector Axial Charge from QCD Sum Rules

The isospin breaking in the nucleon isovector axial charge, $g_A^3$, are calculated within the external field QCD sum-rule approach. The isospin violations arising from the difference in up and down current quark masses and in up and down quark condensates are included; electromagnetic effects are not considered. We find $\delta g^3_A/g^3_A \approx (0.5-1.0)\times 10^{-2}$, where $\delta g^3_A = (g^3_A)_p + (g^3_A)_n$ and $ g^3_A = [(g^3_A)_p - (g^3_A)_n]/2$. Using the Goldberger-Treiman relation, we also obtain an estimate of the isospin breaking in the pion-nucleon coupling constant, $(g_{pp\pi_0}-g_{nn\pi_0})/g_{NN\pi} \approx (2-7) \times 10^{-3}$.