Chiral extrapolation of elastic meson-meson scattering: phase shifts and resonance poles

Abstract

We study the dependence of the π π scattering phase shifts on the light quark mass in both standard and unitarized SU(2) Chiral Perturbation Theory (ChPT) to one and two loops. We then use unitarized SU(3) ChPT to study the elastic f_0(600), k(800), ρ(770) and K*(892) resonances. The quark masses are varied up to values of interest for lattice studies. We find a very soft dependence on the light quark mass of the π π phase shifts as a function of the center of mass momentum at one loop and slightly stronger at two loops and a good agreement with lattice results. The SU(3) analysis shows that the properties of the ρ(770) and K*(892) depend smoothly on the quark mass whereas the scalar resonances present a non- analyticity at high quark masses. We also confirm the lattice assumption of quark mass independence of the vector two-meson coupling that, however, is violated for scalars.