Generalized Breit-Wigner expressions describing both single and coupled scalar resonances are derived by combining chiral symmetry and unitarization. Bare scalar propagators are dressed by two-pion loops, results are analytical, and there is little model dependence, since no form factors are used. In the single resonance case, two free coupling parameters are present, which allow flexible descriptions of masses, widths, and pole positions. The usual $K$-matrix unitarization procedure is recovered as an approximation. When two resonances are present, intermediate pion loops give rise to a coupled channel problem and there is no simple relationship between the unitarized amplitude and Breit-Wigner expressions for individual resonances. Eventually, we approximate and generalize our results and give friendly expressions that can be used in the parametrization of scalar resonances in data analyses.

• Received 1 February 2005

DOI:https://doi.org/10.1103/PhysRevD.73.034028