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

We use the one-loop chiral perturbation theory pi pi-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) (sigma) and the rho meson. As the main results, we find that the rho pi pi coupling constant is almost quark mass independent and that the rho mass shows a smooth quark-mass dependence while that of the sigma shows a strong nonanalyticity. These findings are important for studies of the meson spectrum on the lattice.