The positive-parity nucleon spectrum is explored in $2+1$ flavor lattice QCD in a search for new low-lying energy eigenstates near the energy regime of the Roper resonance. In addition to conventional three-quark operators, we consider novel, local five-quark meson-baryon type interpolating fields that hold the promise to reveal new eigenstates that may have been missed in previous analyses. Drawing on phenomenological insight, five-quark operators based on $\sigma N$, $\pi N$ and $a_{0}N$ channels are constructed. Spectra are produced in a high-statistics analysis on the PACS-CS dynamical gauge-field configurations with $m_{\pi }=411\mathrm{MeV}$ via variational analyses of several operator combinations. Despite the introduction of qualitatively different interpolating fields, no new states are observed in the energy regime of the Roper resonance. This result provides further evidence that the low-lying finite-volume scattering states are not localized, and strengthens the interpretation of the Roper as a coupled-channel, dynamically-generated meson-baryon resonance.

• Received 11 August 2016

DOI:https://doi.org/10.1103/PhysRevD.95.074507