Pion Physics at Low Energy and High Accuracy

The role of the quark condensate for the low energy structure of QCD is discussed in some detail. In particular, the dependence of M_pi on m_u and m_d and the low energy theorems for the pi-pi scattering amplitude are reviewed. The new data on Ke4 decay beautifully confirm the standard picture, according to which the quark condensate is the leading order parameter of the spontaneously broken chiral symmetry.Comment: Talk given at the Workshop QCD@Work, Martina Franca, June 200

The Masses of the Light Quarks

Talk given at the Conference on Fundamental Interactions of Elementary Particles, ITEP, Moscow, Oct. 1995. The paper reviews the current status of knowledge concerning m_u, m_d and m_s. Qualitative aspects of the resulting picture for the breaking of isospin and eightfold way symmetries are discussed. At a more quantitative level, the review focuses on the chiral perturbation theory results for the masses of the Goldstone bosons. The corresponding bounds and estimates for the ratios m_u/m_d and m_s/m_d are described in some detail.Comment: 23 pages, 3 figure

Light Quark Effective Theory

Lecture Notes, Summer School on Effective Theories and Fundamental Interactions, Erice, 1996. The application of effective field theory methods to the low energy structure of QCD is discussed. I emphasize the universal structure of the corresponding effective Lagrangian and then discuss the physics of the effective coupling constants. The implications of the effective theory for the masses of the light quarks are analyzed in some detail.Comment: 30 pages, 3 postscript figure

Recent developments in the physics of light quarks

My talk was dedicated to the memory of Jan Stern. The brief account given below focuses on the progress achieved in the determination of the $\pi\pi$ S-wave scattering lengths, both experimentally and with light dynamical quarks on a lattice. In view of the excellent agreement, we can conclude that (a) the expansion in powers of the two lightest quark masses represents a very efficient tool for the analysis of the low energy structure of QCD and (b) the size of the energy gap of QCD is governed by the order parameter of lowest dimension, the quark condensate.Comment: Contribution to Proc. Confinement and the Hadron Spectrum VIII, Mainz, Germany, Sept. 1-6, 200

Light quark masses

Low energy precision experiments provide significant tests of the laws of nature that can reveal physics beyond the Standard Model. A good theoretical understanding of the low energy properties of QCD is required for this purpose. The recent developments at the interface between lattice and effective field theory methods provide an excellent basis for pion physics already now, while the extension required to explore the low energy properties in the strange quark sector yet calls for further work, also in view of a better determination of the light quark masses. At the precision achieved in lattice determination of quark mass ratios, the e.m. self-energies of the mesons play an important role. I point out some unresolved issues occurring in this context and then summarize the present knowledge of the light quark masses.Comment: Contribution to the Proceedings of the Workshop on Chiral Dynamics, Bern, 200

pi-pi scattering: theory is ahead of experiment

I draw attention to a recent breakthrough in the field of low energy pion physics: the consequences of the hidden symmetry of the QCD Hamiltonian have successfully been incorporated in the general dispersive framework for the pi-pi scattering amplitude, which is due to Roy. The meagre experimental information about the imaginary parts at and above 0.8 GeV suffices to unambiguously and accurately pin down the scattering amplitude at lower energies. The recent Brookhaven data on the reaction K -> pi pi e nu provide a significant test of the theory. They imply that the Gell-Mann-Oakes-Renner relation is approximately valid -- the bulk of the pion mass indeed originates in the quark condensate.Comment: Talk given in honour of Arnulfo Zepeda at the X Mexican School of Particles and Fields, Playa del Carmen, Mexico, 2002, 8 p