Pion-nucleon scattering in the Roper channel from lattice QCD

Abstract

We present a lattice QCD study of Nπ scattering in the positive-parity nucleon channel, where the puzzling Roper resonance N∗(1440) resides in experiment. The study is based on the PACS-CS ensemble of gauge configurations with Nf=2+1 Wilson-clover dynamical fermions, mπ≃156 MeV and L≃2.9 fm. In addition to a number of qqq interpolating fields, we implement operators for Nπ in p-wave and Nσ in s-wave. In the center-of-momentum frame we find three eigenstates below 1.65 GeV. They are dominated by N(0), N(0)π(0)π(0) [mixed with N(0)σ(0)] and N(p)π(-p) with p≃2π/L, where momenta are given in parentheses. This is the first simulation where the expected multi-hadron states are found in this channel. The experimental Nπ phase shift would - in the approximation of purely elastic Nπ scattering - imply an additional eigenstate near the Roper mass mR≃1.43 GeV for our lattice size. We do not observe any such additional eigenstate, which indicates that Nπ elastic scattering alone does not render a low-lying Roper. Coupling with other channels, most notably with Nππ, seems to be important for generating the Roper resonance, reinforcing the notion that this state could be a dynamically generated resonance. Our results are in line with most of the previous lattice studies based just on qqq interpolators, which did not find a Roper eigenstate below 1.65 GeV. The study of the coupled-channel scattering including a three-particle decay Nππ remains a challenge.