Understanding the 1P- and 2S-wave nucleon resonances within the extended Lee-Friedrichs Model

TL;DR

This paper models low-lying nucleon resonances using an extended Lee-Friedrichs scheme, explaining the Roper resonance's mass and structure through coupled-channel dynamics and meson-baryon interactions.

Contribution

It introduces a unified framework incorporating coupled-channel effects to accurately reproduce nucleon resonance properties and explain the Roper resonance's level inversion.

Findings

The Roper resonance's pole shifts downward to match experimental mass.

The model reproduces properties of five $1P$-wave resonances.

The Roper resonance has significant meson-baryon continuum components.

Abstract

We present a unified desciption of the low-lying $1P$- and $2S$-wave nucleon resonance within the framework of an extended Lee-Friedrichs scheme. By incorporating the coupled-channel dynamics between bare quark-model states and the $\pi N$, $\pi\Delta$ and $\eta N$ meson-baryon continua, we examine the mass shifts and structural properties of these excited states. We demonstrate that when the model parameters are calibrated to match the $1P$-wave spectrum and their widths, the pole associated with the bare $2S$ state is naturally shifted downward to the mass region of physical Roper resonance--$N(1440)$, thereby offering a dynamical explanation for the long-standing level-inversion problem. An approximate analysis of compositeness and elementariness reveals that the Roper resonance contains a significant meson-baryon continuum states, consistent with the picture of a bare core heavily dressed by meson-baryon cloud. Simultaneously, the pole positions and properties of five $1P$-wave resonances--$N(1535)$, $N(1650)$, $N(1520)$, $N(1700)$ and $N(1675)$ are successfully reproduced. Our results highlight the essential role of coupled-channel effects in shaping the nucleon spectrum and provide a consistent microscopic insight into the interplay between internal quark degrees of freedom and external hadronic fields.