Finite volume effects and quark mass dependence of the N(1535) and N(1650)

Abstract

For resonances decaying in a finite volume, the simple identification of state and eigenvalue is lost. The extraction of the scattering amplitude is a major challenge as we demonstrate by extrapolating the physical S_{11} amplitude of pion-nucleon scattering to the finite volume and unphysical quark masses, using a unitarized chiral framework including all next-to-leading order contact terms. We show that the pole movement of the resonances N(1535)1/2^- and N(1650)1/2^- with varying quark masses is non-trivial. In addition, there are several strongly coupled S-wave thresholds that induce a similar avoided level crossing as narrow resonances. The level spectrum is predicted for two typical lattice setups, and ways to extract the amplitude from upcoming lattice data are discussed.