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

Abstract

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 ir 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 p contribution to the sum rule for the TT-T scattering. The approach to T e s decay based on dispersion theory and charge-current commutators already used by Marshak et al. for K e z 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.

Superconvergent Bootstrap of the Vector and Tensor Regge Trajectories

“…Rev. Letters 19, 1402(1967] considered a similar problem and derived bootstrap conditions based on GSCR. Their approach, however, is not one of a systematic bootstrap.…”

Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances $$\sigma /f_0(500) $$ and $$\kappa /K_0^*(700) $$

“…But the κ name stuck. The need for a near-threshold κ state besides the K * observed above 1.3 GeV was also required from attempts to saturate the Adler-Weisberger Axial-charge sum rule for πK scattering, although the mass predictions were very crude, ranging from 0.85-1.2 MeV [39] or 500-740 MeV [40]. This predicted state was much wider than 30 MeV, even reaching a 450 MeV width 3 .…”