Mass and width of the sigma

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 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.

Contribution to the proceedings of MESON 2006 (Krakow)

References in corpus (7)

• ππscattering
• Mass and width of the lowest resonance in QCD
• Light pseudoscalar decay constants, quark masses, and low energy constants from three-flavor lattice QCD
• I=2 pi-pi Scattering from Fully-Dynamical Mixed-Action Lattice QCD
• First measurement of the ${\pi }^{+}{\pi }^{-}$ atom lifetime
• Scalar form factors of light mesons
• Rescattering effects and the $\sigma$ pole in hadronic decays

Cited by in corpus (8)

• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• Highly Excited Mesons, Linear Regge Trajectories and the Pattern of the Chiral Symmetry Realization
• Investigation of a0-f0 mixing
• Vector and axialvector mesons at nonzero temperature within a gauged linear sigma model
• Roper resonances in chiral quark models
• On the $\pi \pi$ contribution to the QCD sum rules for the light tetraquark
• A Calculation of the Physical Mass of Sigma Meson
• Role of the $\sigma$-resonance in determining the convergence of chiral perturbation theory