We present for the first time a determination of the energy dependence of the isoscalar ππ 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 KK threshold. Calculations are performed at two values of the u,d quark mass corresponding to mπ=236,391 MeV and the resulting amplitudes are described in terms of a σ meson which evolves from a bound-state below ππ threshold at the heavier quark mass, to a broad resonance at the lighter quark mass.
@article{arxiv.1607.05900,
title = {Isoscalar $\pi\pi$ scattering and the $\sigma$ meson resonance from QCD},
author = {Raul A. Briceno and Jozef J. Dudek and Robert G. Edwards and David J. Wilson},
journal= {arXiv preprint arXiv:1607.05900},
year = {2017}
}