Axial vector current matrix elements and QCD sum rules

The matrix element of the isoscalar axial vector current, (u) over bar gamma(mu)gamma(5)mu + (d) over bar-gamma(mu)gamma(5)d, between nucleon states is computed using the external field QCD sum rule method. The external field induced correlator, (0 vertical bar(q) over bar gamma(mu)gamma(5)q vertical bar 0), 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 dertermine the matrix element (mu) over bar gamma(mu)gamma(5)u + (d) over bar gamma(mu)gamma(5)d- 2 (s) over bar gamma(mu)gamma(5)s between nucleon states. Combining with our calculation of (u) over bar gamma(mu)gamma(5)u+(d) over bar gamma(mu)gamma(5)d and the well-known nucleon beta-decay constant allows us to determine (p, s vertical bar 4/9 (u) over bar gamma(mu)gamma(5)u+1/9 (d) over bar gamma(mu)gamma(5)d+1/9 (s) over bar gamma(mu)gamma(5)s vertical bar p,s) 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.