A Lattice QCD Study of Pion–Nucleon Scattering in the Roper Channel

We present a lattice QCD study of the puzzling positive-parity nucleon channel, where the Roper resonance \(N^*(1440)\) resides in experiment. The study is based on an ensemble of gauge configurations with \(N_f=2+1\) Wilson-clover fermions with a pion mass of 156 MeV and lattice size \(L=2.9\) fm. We use several qqq interpolating fields combined with \(N\pi \) and \(N\sigma \) two-hadron operators in calculating the energy spectrum in the rest frame. Combining experimental \(N\pi \) phase shifts with elastic approximation and the Luscher formalism suggests in the spectrum an additional energy level near the Roper mass \(m_R=1.43\) GeV for our lattice. We do not observe any such additional energy level, which implies that \(N\pi \) elastic scattering alone does not render a low-lying Roper resonance. The current status indicates that the \(N^*(1440)\) might arise as dynamically generated resonance from coupling to other channels, most notably the \(N\pi \pi \).