The Standard Model of particle physics unifies the description of three of the four fundamental forces of Nature. The strong force is responsible for the formation of protons, nuclei, and unstable hadrons like pions and kaons. However, the underlying theory, quantum chromodynamics (QCD), has quarks and gluons as elementary particles and force carriers. Moreover, at low energies, this theory can no longer be solved by perturbative methods.;This challenge is addressed both in experiment and computer-based simulations of QCD, and in both cases an analysis of the resulting data ---mostly obtained from scattering two or more particles--- is required. This thesis aims at enabling and improving the data analysis. Even if the two types of data are in principle very different, they share many aspects and allow for the development and application of similar techniques.;Three-body unitarity is an important property of the S-matrix that should be manifestly fulfilled in the analysis of next-generation spectroscopy measurements of excited mesons at GlueX, COMPASS, BES and other experiments. In this thesis, we formally develop the 3 → 3 scattering amplitude for spinless particles in the isobar-spectator picture. Using a Bethe-Salpeter Ansatz, we derive a relativistic three-dimensional scattering equation that manifestly fulfills three-body unitarity and two-body unitarity for the sub-amplitudes. This property holds for energies above breakup and also in the presence of resonances in the sub-amplitudes. While unitarity is the linchpin for future analyses of experimental and lattice data, the thesis work concentrates on the second aspect: Two-body amplitudes serve as input to the three-body isobar parametrization. In this thesis, we analyze Nf = 2 and Nf = 2 + 1 flavor lattice data on the &rgr;(770) meson using unitarized Chiral Perturbation Theory, allowing not only for the extrapolation in mass but also in flavor. While the chiral extrapolation of Nf = 2 lattice data leads to masses of the &rgr;(770) meson far below the experimental one, we find that the missing KKbar channel can explain this discrepancy.;Besides the &rgr;(770), we also analyze recent results on isoscalar pipi scattering from a Nf = 2 + 1 lattice simulation performing the first chiral extrapolation for this emblematic channel. This work lays the cornerstone for future analyses of three-body systems on the lattice. It is complemented by a more general study of statistical and model selection aspects expected to be relevant in such future analyses.
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