Quark-mass dependence of the ρ and σ mesons from dispersion relations and chiral perturbation theory

We use the one-loop chiral perturbation theory π π -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 f_0(600) (σ) and the ρ meson. As the main results, we find that the rho π π 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