Coupled ππ, K(K)over-bar scattering in P-wave and the ρ resonance from lattice QCD

We determine elastic and coupled-channel amplitudes for isospin-1 meson-meson scattering in P wave, by calculating correlation functions using lattice QCD with light quark masses such that m(pi) = 236 MeV in a cubic volume of similar to(4 fm)(3). Variational analyses of large matrices of correlation functions computed using operator constructions resembling pi pi, K (K) over bar and q (q) over bar, in several moving frames and several lattice irreducible representations, lead to discrete energy spectra from which scattering amplitudes are extracted. In the elastic pp scattering region we obtain a detailed energy dependence for the phase shift, corresponding to a. resonance, and we extend the analysis into the coupled-channel K (K) over bar region for the first time, finding a small coupling between the channels.