Scalar mesons and pi-pi S-wave scattering in a quark model with chiral symmetry

We implement chiral symmetry in quark models, nt the strong-coupling BCS le vel, we perform the crucial and independent tests of studying the scalar-me son decay into a pair of pions and the pi - pi scattering length. We arrive at the Weinberg scattering length. For consistency we have to go beyond th e BCS level of the spontaneous breaking of chiral symmetry. We include coup led channels in the mass-gap equation, and this removes any systematic shif t of the hadron spectrum. We also show that coupled channels reduce the bre aking of chiral symmetry, with the same Feynman diagrams that appear in the coupling of a scalar meson to a pair of pseudoscalar mesons. To compute qu antitative results, we use a lattice-QCD-inspired quark-quark interaction. We find that the ground state I = 0, P-3(0) q (q) over bar meson is the f(0 )(980) with a partial decay width of 40 MeV. We also find a 30% reduction o f the chiral condensate due to coupled channels.