David Greynat

Rare kaon decays revisited

Abstract We present an updated discussion of K→π l l decays in a combined framework of chiral perturbation theory and large- N c QCD, which assumes the dominance of a minimal narrow resonance structure in the invariant mass dependence of the l l 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( K S → π 0 e + e − ) is, within errors, consistent with the recently reported result from the NA48 Collaboration. Predictions for the K → πμ + μ − modes are also obtained. We find that the resulting interference between the direct and indirect CP-violation amplitudes in K L → π 0 e + e − is constructive.

Asymptotics of Feynman diagrams and the Mellin–Barnes representation

Abstract 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.

Chiral condensates, Q(7) and Q(8) matrix elements and large-N(c) QCD

The correlation function of a V−A current with a V+A current is discussed within the framework of QCD in the limit of a large number of colours Nc. Applications to the evaluation of chiral condensates of dimension six and higher, as well as to the matrix elements of the Q7 and Q8 electroweak penguin operators are discussed. A critical comparison with previous determinations of the same parameters has also been made.

On convergent series representations of Mellin-Barnes integrals

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 power series and logarithms of the parameters involved in the problem under consideration. However, in most of the cases, several convergent series representations exist for a given integral. These series 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: First, different sets of poles which correspond to different convergent double series representations of a given integral, second the regions of convergence of all these series (without an a priori full knowledge of their general term), and third the general term of each series (this may be performed, if necessary, once the relevant domain of convergence has been found). Thi...

Chiral Condensates, Q_7 and Q_8 Matrix Elements and Large-N_c QCD

The correlation function of a V−A current with a V+A current is discussed within the framework of QCD in the limit of a large number of colours Nc. Applications to the evaluation of chiral condensates of dimension six and higher, as well as to the matrix elements of the Q7 and Q8 electroweak penguin operators are discussed. A critical comparison with previous determinations of the same parameters has also been made.

Derivatives of the Pochhammer and reciprocal Pochhammer symbols and their use in epsilon-expansions of Appell and Kampé de Fériet functions

Useful expressions of the derivatives, to any order, of Pochhammer and reciprocal Pochhammer symbols with respect to their arguments are presented. They are building blocks of a procedure, recently suggested, for obtaining the ɛ-expansion of functions of the hypergeometric class related to Feynman integrals. The procedure is applied to some examples of such kind of functions taken from the literature.

Chiral condensates, Q7 and Q8 matrix elements and large-Nc QCD

The correlation function of a V−A current with a V+A current is discussed within the framework of QCD in the limit of a large number of colours Nc. Applications to the evaluation of chiral condensates of dimension six and higher, as well as to the matrix elements of the Q7 and Q8 electroweak penguin operators are discussed. A critical comparison with previous determinations of the same parameters has also been made.

The Froissart--Martin Bound for ππ Scattering in QCD

The Froissart--Martin bound for total

Asymptotic behaviour of pion-pion total cross-sections

\pi\pi

The Mellin-Barnes Approach to Hadronic Vacuum Polarization and

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