Composition of low-lying J=32± Δ-baryons

Liu, Langtian; Chen, Chen; Lu, Ya; Roberts, Craig D.; Segovia, Jorge

doi:10.1103/PhysRevD.105.114047

Composition of low-lying $J = {\frac{3}{2}}^{\pm}$ $Δ$ -baryons

Langtian Liu (School of Physics, Nanjing University, Nanjing, Jiangsu 210093, China; Institute for Nonperturbative Physics, Nanjing University, Nanjing, Jiangsu 210093, China) ; Chen Chen (Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui 230026, China; Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, China) ; Ya Lu (School of Physics, Nanjing University, Nanjing, Jiangsu 210093, China; Institute for Nonperturbative Physics, Nanjing University, Nanjing, Jiangsu 210093, China; Department of Physics, Nanjing Tech University, Nanjing 211816, China) ; Craig D. Roberts (School of Physics, Nanjing University, Nanjing, Jiangsu 210093, China; Institute for Nonperturbative Physics, Nanjing University, Nanjing, Jiangsu 210093, China) ; Jorge Segovia (Departamento Sistemas Físicos, Químicos y Naturales, Universidad Pablo de Olavide, E-41013 Sevilla, Spain; Institute for Nonperturbative Physics, Nanjing University, Nanjing, Jiangsu 210093, China)

A Poincaré-covariant $quark + diquark$ Faddeev equation is used to develop insights into the structure of the four lightest $(I, J^{P} = \frac{3}{2}, {\frac{3}{2}}^{\pm})$ baryon multiplets. While these systems can contain isovector-axialvector and isovector-vector diquarks, one may neglect the latter and still arrive at a reliable description. The $(\frac{3}{2}, {\frac{3}{2}}^{+})$ states are the simpler systems, with features that bear some resemblance to quark model pictures, e.g., their most prominent rest-frame orbital angular momentum component is $S$ -wave and the $Δ (1600) {\frac{3}{2}}^{+}$ may reasonably be viewed as a radial excitation of the $Δ (1232) {\frac{3}{2}}^{+}$ . The $(\frac{3}{2}, {\frac{3}{2}}^{-})$ states are more complex: the $Δ (1940) {\frac{3}{2}}^{-}$ expresses little of the character of a radial excitation of the $Δ (1700) {\frac{3}{2}}^{-}$ ; and while the rest-frame wave function of the latter is predominantly $P$ -wave, the leading piece in the $Δ (1940) {\frac{3}{2}}^{-}$ wave function is $S$ -wave, in conflict with quark model expectations. Experiments that can test these predictions, such as large momentum transfer resonance electroexcitation, may shed light on the nature of emergent hadron mass.

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      "value": "A Poincar\u00e9-covariant <math><mrow><mi>quark</mi><mo>+</mo><mi>diquark</mi></mrow></math> Faddeev equation is used to develop insights into the structure of the four lightest <math><mo>(</mo><mi>I</mi><mo>,</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>\u00b1</mo></msup><mo>)</mo></math> baryon multiplets. While these systems can contain isovector-axialvector and isovector-vector diquarks, one may neglect the latter and still arrive at a reliable description. The <math><mo>(</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>+</mo></msup><mo>)</mo></math> states are the simpler systems, with features that bear some resemblance to quark model pictures, e.g., their most prominent rest-frame orbital angular momentum component is <math><mi>S</mi></math>-wave and the <math><mrow><mi>\u0394</mi><mo>(</mo><mn>1600</mn><mo>)</mo><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> may reasonably be viewed as a radial excitation of the <math><mi>\u0394</mi><mo>(</mo><mn>1232</mn><mo>)</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>+</mo></msup></math>. The <math><mo>(</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>\u2212</mo></msup><mo>)</mo></math> states are more complex: the <math><mi>\u0394</mi><mo>(</mo><mn>1940</mn><mo>)</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>\u2212</mo></msup></math> expresses little of the character of a radial excitation of the <math><mi>\u0394</mi><mo>(</mo><mn>1700</mn><mo>)</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>\u2212</mo></msup></math>; and while the rest-frame wave function of the latter is predominantly <math><mi>P</mi></math>-wave, the leading piece in the <math><mi>\u0394</mi><mo>(</mo><mn>1940</mn><mo>)</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>\u2212</mo></msup></math> wave function is <math><mi>S</mi></math>-wave, in conflict with quark model expectations. Experiments that can test these predictions, such as large momentum transfer resonance electroexcitation, may shed light on the nature of emergent hadron mass."
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Published on:: 27 June 2022
Publisher:: APS
Published in:: Physical Review D , Volume 105 (2022)
Issue 11
DOI:: https://doi.org/10.1103/PhysRevD.105.114047
arXiv:: 2203.12083
Copyrights:: Published by the American Physical Society
Licence:: CC-BY-4.0

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