The Roper resonance: a genuine quark state or a dynamically generated structure?

TL;DR

This paper investigates whether the Roper resonance is a genuine three-quark state or a dynamically generated structure, using a coupled channel approach and lattice QCD insights.

Contribution

It introduces a coupled channel model incorporating phenomenological sigma interactions and explores the interplay between dynamically generated states and three-quark resonances.

Findings

A quasi-bound state emerges around 1.4 GeV with strong sigma coupling.

The resonance's mass is primarily determined by the dynamically generated state if the three-quark state is above 1.6 GeV.

Including the three-quark state is essential for matching experimental width and pole modulus.

Abstract

In view of the recent results of lattice QCD simulation in the P11 partial wave that has found no clear signal for the three-quark Roper state we investigate a different mechanism for the formation of the Roper resonance in a coupled channel approach including the $\pi N$, $\pi\Delta$ and $\sigma N$ channels. We fix the pion-baryon vertices in the underlying quark model while the $s$-wave sigma-baryon interaction is introduced phenomenologically with the coupling strength, the mass and the width of the $\sigma$ meson as free parameters. The Laurent-Pietarinen expansion is used to extract the information about the $S$-matrix pole. The Lippmann-Schwinger equation for the $K$ matrix with a separable kernel is solved to all orders. For sufficiently strong $\sigma NN$ coupling the kernel becomes singular and a quasi-bound state emerges at around 1.4~GeV, dominated by the $\sigma N$ component and reflecting itself in a pole of the $S$-matrix. The alternative mechanism involving a $(1s)^22s$ quark resonant state is added to the model and the interplay of the dynamically generated state and the three-quark resonant state is studied. It turns out that for the mass of the three-quark resonant state above 1.6~GeV the mass of the resonance is determined solely by the dynamically generated state, nonetheless, the inclusion of the three-quark resonant state is imperative to reproduce the experimental width and the modulus of the resonance pole.