A lattice QCD study of pion-nucleon scattering in the Roper channel

Abstract

We present a lattice QCD study of the puzzling positive-parity nucleon channel, where the Roper resonance $N^{\ast }(1440)$ 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 Lüscher 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 $N^{\ast }(1440)$ might arise as dynamically generated resonance from coupling to other channels, most notably the $N\pi \pi$.

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