Zachary T. Draper

We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of π + and K + , at a lattice spacing a = 0.063 fm , and in the isospin-symmetric limit. We also obtain accurate results for maximal-isospin two-meson amplitudes, with those for π + K + and 2 K + being the first determinations at the physical point. Dense lattice spectra are obtained using the stochastic Laplacian-Heaviside method, and the analysis leading to scattering amplitudes is done using the relativistic finite-volume formalism. Results are compared to chiral perturbation theory and to phenomenological fits to experimental data, finding good agreement.

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.

We generalize the relativistic field-theoretic (RFT) three-particle finite-volume formalism to systems of three identical, massive, spin-1/2 fermions, such as three neutrons. This allows, in principle, for the determination of the three-neutron interaction from the finite-volume spectrum of three-neutron states, which can be obtained from lattice QCD calculations.

We generalize the relativistic field-theoretic (RFT) three-particle finite-volume formalism to systems of three identical, massive, spin-$1/2$ fermions, such as three neutrons. This allows, in principle, for the determination of the three-neutron interaction from the finite-volume spectrum of three-neutron states, which can be obtained from lattice QCD calculations.

We study the interactions of systems of two and three nondegenerate mesons composed of pions and kaons at maximal isospin using lattice QCD, specifically π⁺K⁺, π⁺π⁺K⁺ and K⁺K⁺π⁺. Utilizing the stochastic LapH method, we determine the spectrum of these systems on two CLS N_f = 2 + 1 ensembles with pion masses of 200 MeV and 340 MeV, and include many levels in different momentum frames. We constrain the K matrices describing two- and three-particle interactions by fitting the spectrum to the results predicted by the finite-volume formalism, including up to p waves. This requires also results for the π⁺π⁺ and K⁺K⁺ spectrum, which have been obtained previously on the same configurations. We explore different fitting strategies, comparing fits to energy shifts with fits to energies boosted to the rest frame, and also comparing simultaneous global fits to all relevant two- and three-particle channels to those where we first fit two-particle channels and then add in the three-particle information. We provide the first determination of the three-particle K matrix in π⁺π⁺K⁺ and K⁺K⁺π⁺ systems, finding statistically significant nonzero results in most cases. We include s and p waves in the K matrix for π⁺K⁺ scattering, finding evidence for an attractive p-wave scattering length. We compare our results to Chiral Perturbation Theory, including an investigation of the impact of discretization errors, for which we provide the leading order predictions obtained using Wilson Chiral Perturbation Theory.