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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We consider deeply virtual Compton scattering on a photon target, in the generalized Bjorken limit, at the Born order and in the leading logarithmic approximation. We interpret the result as a factorized amplitude of a hard process described by handbag diagrams and anomalous generalized parton distributions in the photon. This anomalous part, with its characteristic ln(Q 2 ) dependence, is present both in the DGLAP and in the ERBL regions. As a consequence, these generalized parton distributions of the photon obey DGLAP-ERBL evolution equations with an inhomogeneous term.

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We present an analytic representation of F K =F π as calculated in three-flavor two-loop chiral perturbation theory, which involves expressing three mass scale sunsets in terms of Kampé de Fériet series. We demonstrate how approximations may be made to obtain relatively compact analytic representations. An illustrative set of fits using lattice data is also presented, which shows good agreement with existing fits.

Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple series in powers and logarithms of the parameters involved in the problem under consideration. However, in most of the cases, several series representations exist for a given integral. They converge in different regions of values of the parameters, and it is not obvious to obtain them. For twofold integrals we present a method which allows to derive straightforwardly and systematically: (a) different sets of poles which correspond to different convergent double series representations of a given integral, (b) the regions of convergence of all these series (without an a priori full knowledge of their general term), and (c) the general term of each series (this may be performed, if necessary, once the relevant domain of convergence has been found). This systematic procedure is illustrated with some integrals which appear, among others, in the calculation of the two-loop hexagon Wilson loop in N = 4 SYM theory. Mellin-Barnes integrals of higher dimension are also considered.Comment: 49 pages, 16 figure