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

TL;DR

This lattice QCD study investigates the Roper resonance in pion-nucleon scattering, finding no additional energy level in the spectrum and suggesting the resonance may arise from coupled channels like Nππ.

Contribution

First lattice QCD analysis using multiple interpolating fields and Lüscher formalism to study the Roper resonance in the positive-parity nucleon channel.

Findings

No additional energy level near the Roper mass in the lattice spectrum.

Nπ elastic scattering alone does not produce the low-lying Roper resonance.

The Roper may be a dynamically generated resonance from coupled channels.

Abstract

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 L\"uscher 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 $N\pi\pi$.