pi pi scattering, pion form factors and chiral perturbation theory

I discuss recent progress in our understanding of the pi pi scattering amplitude at low energy thanks to the combined use of chiral perturbation theory and dispersion relations. I also comment on the criticism raised by Pelaez and Yndurain on this work.Comment: 10 pages, 5 figures. Invited talk at the "Quark Confinement and the Hadron Spectrum" VI Conference, Villasimius, Sardinia, Italy, 21-25 September 200

Theoretical progress on pi pi scattering lengths and phases

pi pi scattering at low energy is sensitive to the structure of the QCD vacuum. I review the calculations of the pi pi scattering lengths and phases, and group them in three cathegories: 1. those based on very general theoretical constraints (like dispersion relations and crossing symmetry) and phenomenology, 2. those which in addition make explicit use of chiral symmetry, 3. the first-principle ones, done with lattice QCD. I then compare these to the experimental results. Thanks to recent progress in all these and in the experimental determination of the scattering lengths we are improving substantially our knowledge of the QCD vacuum.Comment: 11 pages, talk given at the KAON International Conference, May 21-25 2007 Laboratori Nazionali di Frascati dell'INFN, Rome, Ital

Pion loops in quenched Quantum Chromodynamics

We calculate the divergences of the generating functional of quenched Chiral Perturbation Theory to one loop for a generic number of flavours. The flavour number dependence of our result enlightens the mechanism of quark loop cancellation in the quenched effective theory for any Green function or S matrix element. We also apply our results to $\pi \pi$ scattering and evaluate the coefficient of the chiral log in the S-wave scattering lengths for the quenched case.Comment: Latex, 10 pages, 1 figur

An introduction to CHPT

These lectures provide an elementary introduction to Chiral Perturbation Theory, focused on the sector of pseudoscalar meson interactions. Basic concepts and technical methods of this approach are discussed on general grounds and with the help of a few specific examples.Comment: 45 pages, Latex. Lectures given at at the 2000 LNF Spring School, Frascati, Italy, 15-20 May 200

A New Dispersive Analysis of eta --> 3 pi

We present a new dispersive analysis of the isospin breaking decay eta --> 3 pi. The resulting representation of the decay amplitude allows us to determine the quark mass double ratio Q and we find as a preliminary result Q = 22.3 +/- 0.4. Finally, we discuss a number of improvements that we intend to implement in the future.Comment: 9 pages, 4 figures, to be published in the proceedings of 6th International Workshop on Chiral Dynamics, CD09, July 6-10, 2009, Bern, Switzerlan

Theory of pi pi scattering

I describe the current status of the theory of pi pi scattering, reviewing in particular recent work on the numerical solution of Roy equations and on the matching between these and the chiral representation. I discuss numerical results on the scattering lengths and other threshold parameters.Comment: Latex 12 pages, Invited plenary talk at Chiral Dynamics 2000, 17-22 July, Jefferson La

Theoretical Aspects of the Pion-Pion Interaction

We give a brief review of the theoretical description of low energy pion-pion scattering by the combined use of Chiral Perturbation Theory and Roy equations, an update of the Regge parametrization of $\pi\pi$ cross sections at high energies, and a short discussion of the scalar radius of the pion.Comment: 4 pages, talk presented by I. Caprini at the International Conference on QCD and Hadronic Physics, June 16-20 2005, Beijin