Novel analysis method for excited states in lattice QCD: The nucleon case

We employ a novel method to analyze Euclidean correlation functions entering the calculation of hadron energies in lattice QCD. The method is based on the sampling of all possible solutions allowed by the spectral decomposition of the hadron correlators. We demonstrate the applicability of the method by studying the nucleon excited states in the positive and negative parity channels over a pion mass range of about 400~MeV to 150~MeV. The results are compared to the standard variational approach routinely used to study excited states within lattice QCD. The main advantage of our new approach is its ability to unambiguously determine all excited states for which the Euclidean time correlation function is sensitive on.