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We demonstrate how heavy mass methods, previously applied to chiral perturbation theory calculations involving the interactions of nucleons and pions, can be generalized to include interactions with the ∆(1232) in a systematic formalism which we call the "small scale expansion".

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Using extended Khuri-Treiman equations, we evaluate the final state interactions due to two-pion rescatterings to the decays η → π 0 π + π − and η → π 0 π 0 π 0 . As subtraction to the dispersion relation we take the one-loop chiral perturbation theory result of Gasser and Leutwyler. The calculated corrections are moderate and amount to about 14% in the amplitude at the center of the decay region. A careful analysis of the errors inherent to our approach is given. As a consequence, the experimental rate of the decay can only be reproduced if the double quark mass ratio Q −2 ≡ m d −mu ms−m · m d +mu ms+m is increased from the usual value of 1/(24.1) 2 to 1/(22.4 ± 0.9) 2 . We have also calculated the ratio of the rates of the two decays and various Dalitz Plot parameters. In particular, the linear slope a in the charged decay is different from the one-loop value and agrees better with experiment.

We consider the weak interaction of the octet of pseudoscalar mesons with meson resonances with spin 0,1 to lowest order in the derivative expansion. We determine the resonance contributions to the O(p 4 ) weak coupling constants. In general, the resonance contributions imply only relations between these constants. If additional assumptions such as factorization or weak deformation are imposed, a more detailed comparison with experiment becomes possible. In contrast to the strong sector, available data do not suggest that all the weak couplings of the p 4 -Lagrangian are dominated by resonance exchange in the factorization approximation. We also give a treatment of singlet external fields.