Quark-Mass Dependence of theρandσMesons from Dispersion Relations and Chiral Perturbation Theory

We use the one-loop chiral perturbation theory ππ-scattering amplitude and dispersion theory in the form of the inverse amplitude method to study the quark-mass dependence of the two lightest resonances of the strong interactions, the f₀(600) (σ) and the ρ meson. As the main results, we find that the ρππ coupling constant is almost quark mass independent and that the ρ mass shows a smooth quark-mass dependence while that of the σ shows a strong nonanalyticity. These findings are important for studies of the meson spectrum on the lattice.