ππscattering

We demonstrate that, together with the available experimental information, chiral symmetry determines the low energy behaviour of the $\pi\pi$ scattering amplitude to within very small uncertainties. In particular, the threshold parameters of the S-, P-, D- and F-waves are predicted, as well as the mass and width of the $\rho$ and of the broad bump in the S-wave. The implications for the coupling constants that occur in the effective Lagrangian beyond leading order and also show up in other processes, are discussed. Also, we analyze the dependence of various observables on the mass of the two lightest quarks in some detail, in view of the extrapolations required to reach the small physical masses on the lattice. The analysis relies on the standard hypothesis, according to which the quark condensate is the leading order parameter of the spontaneously broken symmetry. Our results provide the basis for an experimental test of this hypothesis, in particular in the framework of the ongoing DIRAC experiment: The prediction for the lifetime of the ground state of a $\pi^+\pi^-$ atom reads $\tau=(2.90\pm 0.10)10^{-15} sec$.