DOE OSTI2025
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 𝐽 𝑃 = 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.