A chiral unitary approach for antikaon-nucleon scattering in on-shell factorization is studied. We find multiple sets of parameters for which the model describes all existing hadronic data similarly well. We confirm the two-pole structure of the Λ(1405). The narrow Λ(1405) pole appears at comparable positions in the complex energy plane, whereas the location of the broad pole suffers from a large uncertainty. In the second step, we use a simple model for photoproduction of K + πΣ off the proton and confront it with the experimental data from the CLAS collaboration. It is found that only a few of the hadronic solutions allow for a consistent description of the CLAS data within the assumed reaction mechanism.

The physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativistic 3 → 3 amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two-and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. The corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.

The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. In this study we start from the 3 → 3 scattering amplitude for spinless particles, which contains an isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the latter, 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.

We perform a combined analysis of antikaon-nucleon scattering cross sections and the recent SIDDHARTA kaonic hydrogen data in the framework of a coupled-channel Bethe-Salpeter approach at next-to-leading order in the chiral expansion of the effective potential. We find a precise description of the antikaon-proton scattering amplitudes and are able to extract accurate values of the scattering lengths, a 0 = −1.81 +0.30 −0.28 + i 0.92 +0.29 −0.23 fm , a 1 = +0.48 +0.12 −0.11 + i 0.87 +0.26 −0.20 fm. We also discuss the two-pole structure of the Λ(1405).

The ab initio understanding of hadronic three-body systems above threshold, such as exotic resonances or the baryon spectrum, requires the mapping of the finite-volume eigenvalue spectrum, produced in lattice QCD calculations, to the infinite volume. We present the first application of such a formalism to a physical system in form of three interacting positively charged pions. The results for the ground state energies agree with the available lattice QCD results by the NPLQCD collaboration at unphysical pion masses. Extrapolations to physical pion masses are performed using input from effective field theory. The excited energy spectrum is predicted. This demonstrates the feasibility to determine three-body amplitudes above threshold from lattice QCD, including resonance properties of axial mesons, exotics, and excited baryons.