We study the coupled $\pi N$ system (negative parity, isospin $\frac{1}{2}$) based on a lattice QCD simulation for $n_f=2$ mass degenerate light quarks. Both standard 3-quark baryon operators as well as meson-baryon ($4+1$)-quark operators are included. This is an exploratory study for just one lattice size and lattice spacing and at a pion mass of 266 MeV. Using the distillation method and variational analysis we determine energy levels of the lowest eigenstates. Comparison with the results of simple 3-quark correlation studies exhibits drastic differences and a new level appears. A clearer picture of the negative parity nucleon spectrum emerges. For the parameters of the simulation we may assume elastic $s$-wave scattering and can derive values of the phase shift.

• Received 20 December 2012

DOI:https://doi.org/10.1103/PhysRevD.87.054502