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

A Dispersive Treatment of Kℓ4K_{\ell4} Decays

$K_{\ell4}$ decays offer several reasons of interest: they allow an accurate measurement of $\pi\pi$-scattering lengths; they provide the best source for the determination of some low-energy constants of ChPT; one form factor is directly related to the chiral anomaly, which can be measured here. We present a dispersive treatment of $K_{\ell4}$ decays that provides a resummation of $\pi\pi$- and $K\pi$-rescattering effects. The free parameters of the dispersion relation are fitted to the data of the high-statistics experiments E865 and NA48/2. The matching to ChPT at NLO and NNLO enables us to determine the LECs $L_1^r$, $L_2^r$ and $L_3^r$. With recently published data from NA48/2, the LEC $L_9^r$ can be determined as well. In contrast to a pure chiral treatment, the dispersion relation describes the observed curvature of one of the form factors, which we understand as a rescattering effect beyond NNLO.Comment: 86 pages, 21 figures. Draws on and extends arXiv:1412.5171 [hep-ph] and arXiv:1209.0755 [hep-ph

The pion and proton mass in finite volume

We calculate the finite volume effects for the pion and nucleon mass. For the pion mass we present the results of a full two-loop calculation in chiral perturbation theory. The outcome shows that the resummed version of the Luscher formula we presented in an earlier work does indeed give an excellent approximation to the two-loop result. In view of this result we apply the same resummed formula to the nucleon mass. In the nucleon sector the extension of the chiral expansion to higher quark masses appears to be more problematic and it is therefore more difficult to make reliable predictions for the size of the finite volume effects. We present some preliminary numerical estimates.Comment: 10 pages, 3 figures, Talk given at the Workshop on Computational Hadron Physics, Cyprus, September 14-17, 200