Mass and width of the sigma
  I report on recent work done in collaboration with Irinel Caprini and Gilberto Colangelo. We observe that the Roy equations lead to a representation of the pion pion scattering amplitude that exclusively involves observable quantities, but is valid for complex values of s. At low energies, this representation is dominated by the contributions from the two subtraction constants, which are known to remarkable precision from the low energy theorems of chiral perturbation theory. Evaluating the remaining contributions on the basis of the available data, we demonstrate that the lowest resonance carries the quantum numbers of the vacuum and occurs in the vicinity of the threshold. Although the uncertainties in the data are substantial, the pole position can be calculated quite accurately, because it occurs in the region where the amplitude is dominated by the subtractions. The calculation neatly illustrates the fact that the dynamics of the Goldstone bosons is governed by the symmetries of QCD. 
H. Leutwyler