Abstract
The set of all soft-meson theorems for all scattering amplitudes of the pseudoscalar octet, with two particles off shell, employing PCAC for each pseudoscalar state, current algebra and the σ-terms following from (3, 3) + ( 3,3) breaking of chiral SU(3) × SU(3) symmetry are given. The approximation to the scattering amplitude in the low-energy region by a linear expansion in the invariants is uniquely determined by the absence of exotic σ terms for ππ (as was first shown by Weinberg) πK and KK scattering, when the F π = F K is also required for consistency. To derive the linear expansions for amplitudes involving the η, (3, 3) + ( 3,3) breaking i used in an essential manner; then the value of the symmetry breaking parameter c given by Gell-Mann, Oakes and Renner, the coupling of scalar densities to pseudoscalar states and the usual octet mass formula are naturally recovered. The application of the Adler consitency condition to the Veneziano formulae for pseudoscalar scattering, and its connection with chiral symmetry, are discussed. It is shown that the Adler condition can be justified only when there are exotic channels present.
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