pi pi scattering

We demonstrate that, together with the available experimental information, chiral symmetry determines the low energy behaviour of the pi pi. scatterin g amplitude to within very small uncertainties. In particular, the threshol d parameters of the S-, P-, D- and F-waves are predicted, as well as the ma ss and width of the p and of the broad bump in the S-wave. The implications for the coupling constants that occur in the effective Lagrangian beyond l eading order and also show up in other processes, are discussed. Also, we a nalyze the dependence of various observables on the mass of the two lightes t quarks in some detail, in view of the extrapolations required to reach th e small physical masses on the lattice. The analysis relies on the standard hypothesis, according to which the quark condensate is the leading order p arameter of the spontaneously broken symmetry. Our results provide the basi s fur an experimental test of this hypothesis, in particular in the framewo rk of the ongoing DIRAC experiment: the prediction for the lifetime of the ground state of a pi (+)pi (-) atom reads tau = (2.9 +/- 0.1) x 10(-15) s. (C) 2001 Elsevier Science B.V. All rights reserved.