Isoscalar pi pi Scattering and the sigma Meson Resonance from QCD

We present for the first time a determination of the energy dependence of the isoscalar pi pi elastic scattering phase shift within a first-principles numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum, we obtain the S-wave phase shift up to the K (K) over bar threshold. Calculations are performed at two values of the u, d quark mass corresponding to m(pi) = 236; 391 MeV, and the resulting amplitudes are described in terms of a sigma meson which evolves from a bound state below the pi pi threshold at the heavier quark mass to a broad resonance at the lighter quark mass