Chiral symmetry and parametrization of scalar resonances

Abstract

The linear $\text{s}$-model is used to study the effects of chiral symmetry in unitarized amplitudes incorporating scalar resonances. When just a single resonance is present, we show that the iteration of a chiral tree amplitude by means of regularized two-pion loops preserves the smallness of $\text{p}\text{p}$ interaction at low energies and estimate the importance of pion off-shell contributions. The inclusion of a second resonance is performed by means of a chiral extension of the linear $\text{s}$-model lagrangian. The new $\text{p}\text{p}$ ampitude at tree level complies with low-energy theorems, depends on a mixing angle and has a zero for a given energy between the resonance masses. The unitarization of this amplitude by means of two-pion loops preserves both its chiral low energy behavior and the position of this zero confirming, in a lagrangian framework, conclusions drawn previously by Törnqvist. Finally, we approximate and generalize our results and give a friendly expression that can be used in the parametrization of $N$ coupled scalar resonances.

Comments: 22 pages, 12 figures