Guided by the large-N C limit of QCD, we construct the most general chiral resonance Lagrangian that can generate chiral low-energy constants up to O(p 6 ). By integrating out the resonance fields, the low-energy constants are parametrized in terms of resonance masses and couplings. Information on those couplings and on the low-energy constants can be extracted by analysing QCD Green functions of currents both for large and small momenta. The chiral resonance theory generates Green functions that interpolate between QCD and chiral perturbation theory. As specific examples we consider the V A P and S P P Green functions.

A comprehensive overview of kaon decays is presented. The Standard Model predictions are discussed in detail, covering both the underlying short-distance electroweak dynamics and the important interplay of QCD at long distances. Chiral perturbation theory provides a universal framework for treating leptonic, semileptonic and nonleptonic decays including rare and radiative modes. All allowed decay modes with branching ratios of at least 10 −11 are analyzed. Some decays with even smaller rates are also included. Decays that are strictly forbidden in the Standard Model are not considered in this review. The present experimental status and the prospects for future improvements are reviewed.

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We present a model-independent analysis of K + → π + ℓ + ℓ − and K S → π 0 ℓ + ℓ − decays, including K → 3π unitarity corrections and a general decomposition of the dispersive amplitude. From the existing data on K + → π + e + e − we predict the ratio R = B(K + → π + µ + µ − )/B(K + → π + e + e − ) to be larger than 0.23, in slight disagreement with the recent measurement R = 0.167 ± 0.036. Consequences for the K ± → π ± e + e − charge asymmetries and for the K L → π 0 e + e − mode are also discussed.

Using the 1/N C expansion scheme and truncating the hadronic spectrum to the lowestlying resonances, we match a meromorphic approximation to the SP P Green function onto QCD by imposing the correct large-momentum falloff, both off-shell and on the relevant hadron mass shells. In this way we determine a number of chiral low-energy constants of O(p 6 ), in particular the ones governing SU (3) breaking in the K ℓ3 vector form factor at zero momentum transfer. The main result of our matching procedure is that the known loop contributions largely dominate the corrections of O(p 6 ) to f + (0). We discuss the implications of our final value f K 0 π − + (0) = 0.984 ± 0.012 for the extraction of V us from K ℓ3 decays.