W-parity, octet dominance and the breaking of chiral symmetry

It is shown that W-invariance together with octet dominance restricts the SU(3) × SU(3) symmetry breaking Lagrangian to the representations (3, ) ( ,3), (6, ) ( ,6), (8,8) and (1,8) (8,1). In a nonlinear model, this Lagrangian predicts that the T = 2, S-wave π-π scattering length is zero; and when fitted to the empirical pion and K-meson masses, it predicts a T = 0 scattering length of 0.26m_π⁻¹. Compared with the (3, ) ( ,3) model, this model gives a larger (by a factor 8/3) nucleon σ-term, in agreement with recent calculations.