The matrix element of the isoscalar axial vector current, [Formula: see text], between nucleon states is computed using the external field QCD sum rule method. The external field induced correlator, [Formula: see text], is calculated from the spectrum of the isoscalar axial vector meson states. Since it is difficult to ascertain, from QCD sum rule for hyperons, the accuracy of validity of flavor SU(3) symmetry in hyperon decays when strange quark mass is taken into account, we rely on the empirical validity of Cabbibo theory to determine the matrix element [Formula: see text] between nucleon states. Combining with our calculation of [Formula: see text] and the well-known nucleon β-decay constant allows us to determine [Formula: see text] occurring in the Bjorken sum rule. The result is in reasonable agreement with experiment. We also discuss the role of the anomaly in maintaining flavor symmetry and validity of OZI rule.
Contribution from the Three-Pion State to the Axial Vector Coupling Constant in β-Decay