Axial Vector Current Matrix Elements and QCD Sum Rules

The matrix element of the isoscalar axial vector current, $\bar{u}γ_μγ_5u + \bar{d}γ_μγ_5d$, between nucleon states is computed using the external field QCD sum rule method. The external field induced correlator, $<0|\bar{q}γ_μγ_5q|0>$, 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 flavour 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 $\bar{u}γ_μγ_5 u + \bar{d}γ_μγ_5 d - 2 \bar{s}γ_μγ_5 s$ between nucleon states. Combining with our calculation of $\bar{u}γ_μγ_5 u + \bar{d}γ_μγ_5 d$ and the well known nucleon $β$-decay constant allows us to determine $< p,s| {4/9}\bar{u}γ_μγ_5 u + {1/9}\bar{d}γ_μγ_5 d + {1/9}\bar{s}γ_μγ_5 s |p, s>$ occuring in the Bjorken sum rule. The result is in reasonable agreement with experiment. We also discuss the role of the anomaly in maintaining flavour symmetry and validity of OZI rule.

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