Chiral extrapolation of light resonances from one and two-loop unitarized chiral perturbation theory versus lattice results

We study the pion mass dependence of the ρ(770) and f₀(600) masses and widths from one and two-loop unitarized chiral perturbation theory (ChPT). We show the consistency of one-loop calculations with lattice results for the M_ρ, f_π, and the isospin-2 scattering length a₂₀. Then, we develop and apply the modified inverse amplitude method formalism for two-loop ChPT. In contrast to the f₀(600), the ρ(770) is rather sensitive to the two-loop ChPT parameters---our main source of systematic uncertainty. We thus provide two-loop unitarized fits constrained by lattice information on M_ρ, f_π, by the qq̄ leading 1/Nc behavior of the ρ and by existing estimates of low-energy constants. These fits yield relatively stable predictions up to m_π300--350 MeV for the ρ coupling and width as well as for all the f₀(600) parameters. We confirm, to two loops, the weak m_π dependence of the ρ coupling and the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation, and the existence of two virtual f₀(600) poles for sufficiently high m_π. At two loops one of these poles becomes a bound state when m_π is somewhat larger than 300 MeV.