Unified study of nucleon and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math> baryon spectra and their strong decays with chiral dynamics

In this work, we systematically study both the mass spectra and strong decays of the nucleon and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Δ</a:mi></a:math> resonances up to the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>N</d:mi><d:mo>=</d:mo><d:mn>2</d:mn></d:math> shell within a unified quark model framework with chiral dynamics. In this framework we achieve a good description of the strong decay properties of the well-established nucleon and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi mathvariant="normal">Δ</f:mi></f:math> resonances. Meanwhile, the mass reversal between <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>N</i:mi><i:mo stretchy="false">(</i:mo><i:mn>1440</i:mn><i:mo stretchy="false">)</i:mo><i:mn>1</i:mn><i:mo>/</i:mo><i:msup><i:mn>2</i:mn><i:mo>+</i:mo></i:msup></i:math> as the first radial excitation state and the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mn>1</m:mn><m:mi>P</m:mi></m:math>-wave nucleon resonances can be explained. We show that the three-body spin-orbit potential arising from the one-gluon exchange can cause a large configuration mixing between <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>N</o:mi><o:mo stretchy="false">(</o:mo><o:mn>1520</o:mn><o:mo stretchy="false">)</o:mo><o:mn>3</o:mn><o:mo>/</o:mo><o:msup><o:mn>2</o:mn><o:mo>−</o:mo></o:msup></o:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>N</s:mi><s:mo stretchy="false">(</s:mo><s:mn>1700</s:mn><s:mo stretchy="false">)</s:mo><s:mn>3</s:mn><s:mo>/</s:mo><s:msup><s:mn>2</s:mn><s:mo>−</s:mo></s:msup></s:math> and is also responsible for the large splitting between <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi mathvariant="normal">Δ</w:mi><w:mo stretchy="false">(</w:mo><w:mn>1600</w:mn><w:mo stretchy="false">)</w:mo><w:mn>1</w:mn><w:mo>/</w:mo><w:msup><w:mn>2</w:mn><w:mo>−</w:mo></w:msup></w:math> and <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mi mathvariant="normal">Δ</bb:mi><bb:mo stretchy="false">(</bb:mo><bb:mn>1700</bb:mn><bb:mo stretchy="false">)</bb:mo><bb:mn>3</bb:mn><bb:mo>/</bb:mo><bb:msup><bb:mn>2</bb:mn><bb:mo>−</bb:mo></bb:msup></bb:math>. Some of these baryon resonances tend to weakly couple to the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mi>N</gb:mi><gb:mi>π</gb:mi></gb:math>, <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>N</ib:mi><ib:mi>η</ib:mi></ib:math>, <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>K</kb:mi><kb:mi mathvariant="normal">Λ</kb:mi></kb:math>, and <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mi>K</nb:mi><nb:mi mathvariant="normal">Σ</nb:mi></nb:math> channels, which may answer the question of why they have not been established in these channels via the <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mi>π</qb:mi><qb:mi>N</qb:mi></qb:math> and <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mi>γ</sb:mi><sb:mi>N</sb:mi></sb:math> scatterings. It shows that these “missing resonances” may have large potentials to be established in the <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:mi>N</ub:mi><ub:mi>π</ub:mi><ub:mi>π</ub:mi></ub:math> final state due to their large decay rates into either the <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:mi mathvariant="normal">Δ</wb:mi><wb:mo stretchy="false">(</wb:mo><wb:mn>1232</wb:mn><wb:mo stretchy="false">)</wb:mo></wb:math> or <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:mn>1</bc:mn><bc:mi>P</bc:mi></bc:math>-wave nucleon resonances via the pionic decays. Further experimental search for their signals in charmonium decays at BESIII is thus strongly recommended. Published by the American Physical Society 2024