Showing papers by "Heinrich Leutwyler published in 2006"

Mass and Width of the Lowest Resonance in QCD

Abstract: We demonstrate that near the threshold, the {pi}{pi} scattering amplitude contains a pole with the quantum numbers of the vacuum- commonly referred to as the {sigma} - and determine its mass and width within small uncertainties. Our derivation does not involve models or parametrizations but relies on a straightforward calculation based on the Roy equation for the isoscalar S wave.

Theoretical Aspects of the Pion-Pion Interaction

Abstract: We give a brief review of the theoretical description of low energy pion-pion scattering by the combined use of Chiral Perturbation Theory and Roy equations, an update of the Regge parametrization of ππ cross sections at high energies, and a short discussion of the scalar radius of the pion

On the lowest resonance of QCD

Abstract: 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 ππ 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