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Baryon resonances coupled to Pion-Nucleon states in lattice QCD

In recent years the study of two particle systems on the lattice has led to excellent results in the meson sector of the QCD spectrum, however baryon resonances mostly remain unexplored. We present a study of pion-nucleon systems as decay product of baryon resonances in different channels, with special focus on the nucleon spectrum. We evaluate the correlation functions of single and multi particle interpolators. All the Wick contributions are explicitly computed and the consequences of reduced symmetries in moving frames are taken into account. We discuss the theoretical setup together with results for $n_f=2$ mass degenerate light quarks.