We present an updated discussion of K → πll decays in a combined framework of chiral perturbation theory and Large-Nc QCD, which assumes the dominance of a minimal narrow resonance structure in the invariant mass dependence of thell pair. The proposed picture reproduces very well, both the experimental K + → π + e + e − decay rate and the invariant e + e − mass spectrum. The predicted Br(KS → π 0 e + e − ) is, within errors, consistent with the recently reported result from the NA48 collaboration. Predictions for the K → π µ + µ − modes are also obtained. We find that the resulting interference between the direct and indirect CP-violation amplitudes in KL → π 0 e + e − is constructive.

It is shown that the integral representation of Feynman diagrams in terms of the traditional Feynman parameters, when combined with properties of the Mellin-Barnes representation and the so called converse mapping theorem, provide a very simple and efficient way to obtain the analytic asymptotic behaviours in both the large and small ratios of mass scales.

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The Froissart-Martin bound for total ππ scattering cross sections is reconsidered in the light of QCD properties such as spontaneous chiral symmetry breaking and the counting rules for a large number of colours N c .

Despite recent developments, there are a number of conceptual issues on the hadronic light-by-light (HLbL) contribution to the muon (g − 2) which remain unresolved. One of the most controversial ones is the precise way in which short-distance constraints get saturated by resonance exchange, particularly in the so-called Melnikov-Vainshtein limit. In this paper we address this and related issues from a novel perspective, employing a warped five-dimensional model as a tool to generate a consistent realization of QCD in the large-N c limit. This approach differs from previous ones in that we can work at the level of an effective action, which guarantees that unitarity is preserved and the chiral anomaly is consistently implemented at the hadronic level. We use the model to evaluate the inclusive contribution of Goldstone modes and axial-vector mesons to the HLbL. We find that both anomaly matching and the Melnikov-Vainshtein constraint cannot be fulfilled with a finite number of resonances (including the pion) and instead require an infinite number of axial-vector states. Our numbers for the HLbL point at a non-negligible role of axial-vector mesons, which is closely linked to a correct implementation of QCD short-distance constraints.

We evaluate, analytically, a specific class of eighth order and tenth order QED contributions to the anomalous magnetic moment of the muon. They are generated by Feynman diagrams involving lowest order vacuum polarization insertions of leptons l ¼ e, , and . The results are given in the form of analytic expansions in terms of the mass ratios m e =m and m =m . We compute as many terms as required by the error induced by the present experimental uncertainty on the lepton masses. We show how the Mellin-Barnes integral representation of Feynman parametric integrals allows for an easy analytic evaluation of as many terms as wanted in these expansions and how its underlying algebraic structure generalizes the standard renormalization group properties. We also discuss the generalization of this technique to the case where two independent mass ratios appear. Comparison with previous numerical and analytic evaluations made in the literature, whenever pertinent, are also made.

Using a method previously developed, based on the Mellin-Barnes transform, we reconstruct the two-point correlators in the vector, axial, scalar and pseudoscalar channels from the Taylor expansion at q 2 = 0, the threshold expansion at q 2 = 4m 2 and the OPE at q 2 → −∞, where m is the heavy quark mass. The reconstruction is analytic and systematic and is controlled by an error function which becomes smaller as more terms in those expansions are known.

With the help of the Mellin-Barnes transform, we show how to simultaneously resum the expansion of a heavy-quark correlator around q 2 = 0 (low-energy), q 2 = 4m 2 (threshold, where m is the quark mass) and q 2 → −∞ (high-energy) in a systematic way. We exemplify the method for the perturbative vector correlator at O(α 2 s ) and O(α 3 s ). We show that the coefficients, Ω(n), of the Taylor expansion of the vacuum polarization function in terms of the conformal variable ω admit, for large n, an expansion in powers of 1/n (up to logarithms of n) that we can calculate exactly. This large-n expansion has a sign-alternating component given by the logarithms of the OPE, and a fixed-sign component given by the logarithms of the threshold expansion in the external momentum q 2 .