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.

We study a model-independent parametrization of the vector pion form factor that arises from the constraints of analyticity and unitarity. Our description should be suitable up to ͱsӍ1.2 GeV and allows a modelindependent determination of the mass of the (770) resonance, M ϭ(775.1Ϯ0.5) MeV. We analyze the experimental data on Ϫ → Ϫ 0 in this framework, and its consequences on the low-energy observables worked out by chiral perturbation theory. An evaluation of the two pion contribution to the anomalous magnetic moment of the muon, a , and to the fine structure constant, ␣(M Z 2 ), is also performed.

We present a systematic procedure to obtain the one-loop low-energy effective Lagrangian resulting from integrating out the heavy fields of a given ultraviolet theory. We show that the matching coefficients are determined entirely by the hard region of the functional determinant involving the heavy fields. This represents an important simplification with respect the conventional matching approach, where the full and effective theory contributions have to be computed separately and a cancellation of the infrared divergent parts has to take place. We illustrate the method with a descriptive toy model and with an extension of the Standard Model with a heavy real scalar triplet. A comparison with other schemes that have been put forward recently is also provided.

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