Resonance Saturation of Axial Charge Commutators,SU(3)Symmetry, and Scalar Mesons

Resonance saturation of axial charge commutators taken between states of the pseudoscalar-meson octet is examined and found to be strongly suggestive of the existence of a $0^{+}$ octet and a $0^{+}$ singlet in the 500-1000-MeV region. The vector-meson contribution to the matrix element of the vector current taken between $K$ and $\pi$ states is shown to give only 50% or so of the experimental value, in contrast to the conclusions of other authors, but in agreement with general SU (3) considerations and the estimate of Adler of the $\rho$ contribution to the sum rule for the $\pi -\pi$ scattering. The approach to ${\pi }_{e3\mathrm{}}$ decay based on dispersion theory and charge-current commutators already used by Marshak et al. for $K_{e3\mathrm{}}$ decay is shown to give good agreement with experiment if vector-meson dominance is assumed. It is pointed out that in both cases the resulting expressions for the form factors at zero momentum transfer differ exactly by a factor of 2 from the corresponding ones obtained in the approach using only commutators of charges.