We study systems of two and three mesons composed of pions and kaons at maximal isospin using four CLS ensembles with a 0. 063\;fm, including one with approximately physical quark masses. Using the stochastic Laplacian-Heaviside method, we determine the energy spectrum of these systems including many levels in different momentum frames and irreducible representations. Using the relativistic two- and three-body finite-volume formalism, we constrain the two and three-meson K matrices, including not only the leading s wave, but also p and d waves. By solving the three-body integral equations, we determine, for the first time, the physical-point scattering amplitudes for 3π^+, 3K^+, π^+π^+ K^+ and K^+ K^+ π^+ systems. These are determined for total angular momentum JP=0^-, 1^+, and 2^-. We also obtain accurate results for 2π^+, π^+ K^+, and 2K^+ phase shifts. We compare our results to Chiral Perturbation Theory, and to phenomenological fits.
Dawid et al. (Tue,) studied this question.
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