An implementation of estimating the two-to-two K-matrix from finite-volume energies based on the Lüscher formalism and involving a Hermitian matrix known as the "box matrix" is described. The method includes higher partial waves and multiple decay channels. Two fitting procedures for estimating the K-matrix parameters, which properly incorporate all statistical covariances, are discussed. Formulas and software for handling total spins up to S = 2 and orbital angular momenta up to L = 6 are obtained for total momenta in several directions. First tests involving ρ-meson decay to two pions include the L = 3 and L = 5 partial waves, and the contributions from these higher waves are found to be negligible in the elastic energy range.

Three-body states are critical to the dynamics of many hadronic resonances. We show that lattice QCD calculations have reached a stage where these states can be accurately resolved. We perform a calculation over a wide range of parameters and find all states below inelastic threshold agree with predictions from a state-of-the-art phenomenological formalism. This also illustrates the reliability of the formalism used to connect lattice QCD results to infinite volume physics. Our calculation is performed using three positively charged pions, with different lattice geometries and quark masses.

The elastic I = 1/2, s-and p-wave kaon-pion scattering amplitudes are calculated using a single ensemble of anisotropic lattice QCD gauge field configurations with N f = 2 + 1 flavors of dynamical Wilson-clover fermions at m π = 230MeV. A large spatial extent of L = 3.7fm enables a good energy resolution while partial wave mixing due to the reduced symmetries of the finite volume is treated explicitly. The p-wave amplitude is well described by a Breit-Wigner shape with parameters m K * /m π = 3.808(18) and g BW K * Kπ = 5. 33(20) which are insensitive to the inclusion of d-wave mixing and variation of the s-wave parametrization. An effective range description of the near-threshold s-wave amplitude yields m π a 0 = −0.353(25).

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