A cross-channel study of pion scattering from lattice QCD

We use a chiral model for pion interactions, in the inverse amplitude formalism, to perform a simultaneous analysis of lattice QCD results for pion-pion scattering in all three isospin channels. The input is the finite-volume two-pion spectrum computed using lattice QCD from six ensembles on lattices elongated in one of the spatial dimensions. A two-flavor dynamical lattice QCD action is used with two quark masses corresponding to a pion mass of 315 MeV and 224 MeV. The spectrum in the elastic region is subjected to a global fit which takes into account full correlations across isospin, pion mass and decay constant. The parameters from the fit are used to perform a chiral extrapolation to the physical point. The cross-channel fit results in a more precise determination of the parameters of the model when compared with single channel fits. We obtain $m_\pi a_0^{I=0}=0.2132(9)$, and $m_\pi a_0^{I=2}=0.0433(2)$ as well as $m_\sigma=443(3)-i221(6)$ MeV and $m_\rho=724(4)-i67(1)$ MeV. Several aspects of scale setting and consistency with previous analyses of lattice QCD results are discussed as well.