We present the three-pion spectrum with maximum isospin in a finite volume determined from lattice QCD, including, for the first time, excited states across various irreducible representations at zero and nonzero total momentum, in addition to the ground states in these channels. The required correlation functions, from which the spectrum is extracted, are computed using a newly implemented algorithm which reduces the number of operations, and hence speeds up the computation by more than an order of magnitude. The results for the I = 3 three-pion and the I = 2 two-pion spectrum are publicly available, including all correlations, and can be used to test the available three-particle finite-volume approaches to extracting three-pion interactions.

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.

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).

We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant s-wave interactions, but also those in d waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle d waves. We use three Nf = 2 + 1 CLS ensembles with pion masses of 200, 280, and 340 MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.