Excited nucleons with chirally improved fermions

We study positive and negative parity nucleons on the lattice using the chirally improved lattice Dirac operator. Our analysis is based on a set of three operators ${\chi }_i$ with the nucleon quantum numbers but in different representations of the chiral group and with different diquark content. We use a variational method to separate the ground state and excited states and determine the mixing coefficients for the optimal nucleon operators in terms of the ${\chi }_i.$ We clearly identify the negative parity resonances $N\left(1535\right)\mathrm{}$ and $N\left(1650\right)\mathrm{}$ and their masses agree well with experimental data. The mass of the observed excited positive parity state is too high to be interpreted as the Roper state. Our results for the mixing coefficients indicate that chiral symmetry is important for $N\left(1535\right)\mathrm{}$ and $N\left(1650\right)\mathrm{}$ states. We confront our data for the mixing coefficients with quark models and provide insights into the physics of the nucleon system and the nature of strong decays.