Two- and three-meson scattering amplitudes with physical quark masses from lattice QCD

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Abstract
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 3 π + , 3 K + , 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 2 π + , π + K + , and 2 K + phase shifts. We compare our results to chiral perturbation theory and to phenomenological fits.
Funding Information
  • U.S. Department of Energy (DE-SC0011637)
  • U.S. Department of Energy (DE-SC0011090)
  • U.S. Department of Energy (DE-SC0021006)
  • U.S. Department of Energy (DE-SC0023598)
  • National Science Foundation (PHY-2209167)
  • National Science Foundation (OAC-1818253)
  • Hawk Family Foundation

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