MODEL INDEPENDENT DETERMINATION OF THE LOWEST RESONANCE OF QCD

Abstract

ππ scattering amplitude that exclusively involves observable quantities, but is valid for complex values of s .A t 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. Pions play a crucial role whenever the strong interaction is involved at low energies ‐ the Standard Model prediction for the muon magnetic moment provides a good illustration. The present talk concerns the remarkable theoretical progress made in low energy pion physics in recent years. From the point of view of dispersion theory, ππ scattering is particularly simple: the s-, t -a ndu-channels represent the same physical process. As a consequence, the real part of the scattering amplitude can be represented as a dispersion integral over the imaginary part and the integral exclusively extends over the physical region. 2 The representation involves two subtraction constants which may be identified with the S-wave scattering lengths a 0,a 2 .T he projection of the amplitude on the partial waves leads