Analytic Approaches to Kaon Physics

Most of the analytic approaches which are used at present to understand the low energy hadronic interactions in Particle Physics, get their inspiration from QCD in the limit of a large number of colors $N_c$. I first illustrate this with the example of the left--right correlation function which is an excellent theoretical laboratory. Next, I present the list of observables which have been computed using a large--$N_c$ QCD approach. Finally, I discuss in some detail examples which are relevant to lattice QCD, in the sense that we can make comparisons.Comment: Plenary talk at the Lattice 2002 Conferenc

Update of the Electron and Muon g-Factors

I give an overview of the different contributions to the electron and muon anomalous magnetic moments in the Standard Model. Special emphasis is given to recent QED results as well as to the hadronic light-by-light scattering contribution to the muon anomaly.Comment: Talk given at the QCD-12 Conference in Montpellie

Moment Analysis of Hadronic Vacuum Polarization - Proposal for a lattice QCD evaluation of gμ−2g_{\mu}-2

I suggest a new approach to the determination of the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon $a_{\mu}^{\rm HVP}$ in lattice QCD. It is based on properties of the Mellin transform of the hadronic spectral function and their relation to the HVP self energy in the Euclidean. I show how $a_{\mu}^{\rm HVP}$ is very well approximated by a few moments associated to this Mellin transform and how these moments can be evaluated in lattice QCD, providing thus a series of tests when compared with the corresponding determinations using experimental data

Large-Nc QCD and Low Energy Interactions

This talk reviews recent progress in formulating the dynamics of the electroweak interactions of hadrons at low energies, within the framework of the 1/Nc-expansion in QCD. The emphasis is put on the basic issues of the approach.Comment: Invited talk at the QCD Workshop in Martina Franc

Large-Nc Methods in Kaon Physics

This talk reviews recent progress in formulating the dynamics of Kaon Physics, within the framework of the 1/Nc-expansion in QCD.Comment: 14 pages, 1 figure. Invited talk at the KAON 2001 Conferenc

The Muon g-2 Revisited

I present a short review of the present status of the Standard Model prediction of the anomalous magnetic moment of the muon, with special emphasis on the hadronic contributions.Comment: Invited talk at the XVI Rencontres de Physique at La Thuil

Hadronic Vacuum Polarization in QCD and its Evaluation in the Euclidean

We discuss a new technique to evaluate integrals of QCD Green's functions in the Euclidean based on their Mellin-Barnes representation. We present as a first application the evaluation of the lowest order Hadronic Vacuum Polarization (HVP) contribution to the anomalous magnetic moment of the muon $\frac{1}{2}(g_{\mu}-2)_{\rm\tiny HVP}\equiv a_{\mu}^{\rm HVP}$. It is shown that with a precise determination of the slope and curvature of the HVP function at the origin from lattice QCD (LQCD), one can already obtain a result for $a_{\mu}^{\rm HVP}$ which may serve as a test of the determinations based on experimental measurements of the $e^+ e^-$ annihilation cross-section into hadrons.Comment: Comments added. References added. Typos corrected. Version to be published in the Physical Review

Time delay and short-range scattering in quantum waveguides

Although many physical arguments account for using a modified definition of time delay in multichannel-type scattering processes, one can hardly find rigorous results on that issue in the literature. We try to fill in this gap by showing, both in an abstract setting and in a short-range case, the identity of the modified time delay and the Eisenbud-Wigner time delay in waveguides. In the short-range case we also obtain limiting absorption principles, state spectral properties of the total Hamiltonian, prove the existence of the wave operators and show an explicit formula for the S-matrix. The proofs rely on stationary and commutator methods