Partially Conserved Axial-Vector Current and theπ0→2γDecay Rate

Abstract

The difference between applying partial conservation of axial-vector current (PCAC) to the amplitude for ${\pi }^0\to 2\gamma$ decay, which involves products of local currents, and to amplitudes involving composite hadrons, where it has enjoyed its notable successes-viz., the Goldberger-Treiman relation, the Adler-Weisberger sum rule, and the Adler consistency condition-is analyzed. Using the Bell-Jackiw-Adler theory of the PCAC anomaly, we show that this difference provides a mechanism for removing the factor-of-10 discrepancy that is usually claimed to exist between the observed decay rate and the one calculated on the basis of the original Gell-Mann-Zweig quark model with one triplet of fractionally charged quarks. An essential dynamical assumption is that pion-pole dominance is valid only for those matrix elements of the divergence of the axial-vector current taken with composite hadronic states; this is akin to features in the "weak PCAC" of Brandt and Preparata. A specific model of the hadron as a Bethe-Salpeter bound state of two pointlike constituents is used to illustrate the underlying dynamical mechanism. It follows from this that there should be a sizable enhancement above the PCAC prediction by Adler for forward-angle high-energy very inelastic neutrino-hadron cross sections. Verification of this prediction will be a crucial test of our theory.