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

This is the authors' abstract. We don't add key points for this paper.

We present a unified description of the low-lying <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>1</a:mn> <a:mi>P</a:mi> </a:math> - and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mn>2</c:mn> <c:mi>S</c:mi> </c:math> -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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>π</e:mi> <e:mi>N</e:mi> </e:math> , <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>π</g:mi> <g:mi mathvariant="normal">Δ</g:mi> </g:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>η</j:mi> <j:mi>N</j:mi> </j:math> 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 <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mn>1</l:mn> <l:mi>P</l:mi> </l:math> -wave spectrum and their widths, the pole associated with the bare <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mn>2</n:mn> <n:mi>S</n:mi> </n:math> state is naturally shifted downward to the mass region of physical Roper resonance– <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mi>N</p:mi> <p:mo stretchy="false">(</p:mo> <p:mn>1440</p:mn> <p:mo stretchy="false">)</p:mo> </p:math> , 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 <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mn>1</t:mn> <t:mi>P</t:mi> </t:math> -wave resonances– <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mi>N</v:mi> <v:mo stretchy="false">(</v:mo> <v:mn>1535</v:mn> <v:mo stretchy="false">)</v:mo> </v:math> , <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mi>N</z:mi> <z:mo stretchy="false">(</z:mo> <z:mn>1650</z:mn> <z:mo stretchy="false">)</z:mo> </z:math> , <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:mi>N</db:mi> <db:mo stretchy="false">(</db:mo> <db:mn>1520</db:mn> <db:mo stretchy="false">)</db:mo> </db:math> , <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:mi>N</hb:mi> <hb:mo stretchy="false">(</hb:mo> <hb:mn>1700</hb:mn> <hb:mo stretchy="false">)</hb:mo> </hb:math> and <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:mi>N</lb:mi> <lb:mo stretchy="false">(</lb:mo> <lb:mn>1675</lb:mn> <lb:mo stretchy="false">)</lb:mo> </lb:math> —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.