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.

• Received 18 January 2008

DOI:https://doi.org/10.1103/PhysRevLett.100.152001