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Investigating Fully Strange Tetraquark System with Positive Parity in a Chiral Quark Model
oleh: Yue Tan, Yuheng Wu, Hongxia Huang, Jialun Ping
Format: | Article |
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Diterbitkan: | MDPI AG 2023-12-01 |
Deskripsi
Motivated by the intriguing discovery of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>X</mi><mo>(</mo><mn>6900</mn><mo>)</mo></mrow></semantics></math></inline-formula> by the LHCb collaboration, we undertake a comprehensive study of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></semantics></math></inline-formula> tetraquark system with positive parity, employing the Gaussian expansion within the chiral quark model method. We consider two structures, the diquark–antidiquark (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mi>s</mi></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></semantics></math></inline-formula>) structure and meson–meson (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></semantics></math></inline-formula>) structure, covering all conceivable color and spin configurations. Despite the absence of bound states in our calculations, we have identified potential resonant states with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup></mrow></semantics></math></inline-formula>, namely, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>2150</mn><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>2915</mn><mo>)</mo></mrow></semantics></math></inline-formula>, as well as a resonant state with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></mrow></semantics></math></inline-formula>, denoted as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2950</mn><mo>)</mo></mrow></semantics></math></inline-formula>, and a resonant state with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></semantics></math></inline-formula>, denoted as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>2850</mn><mo>)</mo></mrow></semantics></math></inline-formula>, utilizing the real-scaling method. By comparing their energies and widths, we suggest that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>2915</mn><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2950</mn><mo>)</mo></mrow></semantics></math></inline-formula> may share characteristics with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>X</mi><mo>(</mo><mn>6900</mn><mo>)</mo></mrow></semantics></math></inline-formula>, while <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>2150</mn><mo>)</mo></mrow></semantics></math></inline-formula> could be a promising candidate for the experimental state <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>f</mi><mn>0</mn></msub><mrow><mo>(</mo><mn>2100</mn><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. We strongly advocate for experimental investigations to shed light on the existence and properties of these resonant states.