Studying the Ξ(2030) as a predominantly K¯*Σ</mml:…

Since its discovery in 1977, the spin parity of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Ξ</a:mi><a:mo stretchy="false">(</a:mo><a:mn>2030</a:mn><a:mo stretchy="false">)</a:mo></a:math> has not been fully determined experimentally. The latest Particle Data Group listing suggests it may be a baryon with <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>J</f:mi><f:mo>=</f:mo><f:mn>5</f:mn><f:mo>/</f:mo><f:mn>2</f:mn></f:math>. Therefore, studying the mass spectrum and decay properties of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi mathvariant="normal">Ξ</h:mi><h:mo stretchy="false">(</h:mo><h:mn>2030</h:mn><h:mo stretchy="false">)</h:mo></h:math> has become a current hot topic to definitively establish its spin parity. As the three-quark model fails to explain <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi mathvariant="normal">Ξ</m:mi><m:mo stretchy="false">(</m:mo><m:mn>2030</m:mn><m:mo stretchy="false">)</m:mo></m:math>, we previously proposed it may be a molecule primarily composed of <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msup><r:mover accent="true"><r:mi>K</r:mi><r:mo stretchy="false">¯</r:mo></r:mover><r:mo>*</r:mo></r:msup><r:mi mathvariant="normal">Σ</r:mi></r:math> with <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msup><w:mi>J</w:mi><w:mi>P</w:mi></w:msup><w:mo>=</w:mo><w:mn>5</w:mn><w:mo>/</w:mo><w:msup><w:mn>2</w:mn><w:mo>+</w:mo></w:msup></w:math>, based on its mass spectrum study. To verify its molecular state interpretation, this work proposes studying the strong decays of <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi mathvariant="normal">Ξ</y:mi><y:mo stretchy="false">(</y:mo><y:mn>2030</y:mn><y:mo stretchy="false">)</y:mo></y:math> assuming it is a <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>P</db:mi></db:math>-wave <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:msup><fb:mi>J</fb:mi><fb:mi>P</fb:mi></fb:msup><fb:mo>=</fb:mo><fb:mn>5</fb:mn><fb:mo>/</fb:mo><fb:msup><fb:mn>2</fb:mn><fb:mo>+</fb:mo></fb:msup></fb:math> meson-baryon molecule predominantly composed of <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msup><hb:mover accent="true"><hb:mi>K</hb:mi><hb:mo stretchy="false">¯</hb:mo></hb:mover><hb:mo>*</hb:mo></hb:msup><hb:mi mathvariant="normal">Σ</hb:mi></hb:math>. We calculated all experimentally measured two-body and three-body final state decay widths of <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi mathvariant="normal">Ξ</mb:mi><mb:mo stretchy="false">(</mb:mo><mb:mn>2030</mb:mn><mb:mo stretchy="false">)</mb:mo></mb:math>, including <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:mi mathvariant="normal">Ξ</rb:mi><rb:mo stretchy="false">(</rb:mo><rb:mn>2030</rb:mn><rb:mo stretchy="false">)</rb:mo><rb:mo stretchy="false">→</rb:mo><rb:mover accent="true"><rb:mi>K</rb:mi><rb:mo stretchy="false">¯</rb:mo></rb:mover><rb:mi mathvariant="normal">Λ</rb:mi><rb:mo>,</rb:mo><rb:mover accent="true"><rb:mi>K</rb:mi><rb:mo stretchy="false">¯</rb:mo></rb:mover><rb:mi mathvariant="normal">Σ</rb:mi><rb:mo>,</rb:mo><rb:mi>π</rb:mi><rb:mi mathvariant="normal">Ξ</rb:mi><rb:mo>,</rb:mo><rb:mi>π</rb:mi><rb:msup><rb:mi mathvariant="normal">Ξ</rb:mi><rb:mo>*</rb:mo></rb:msup></rb:math>, and <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"><fc:mi mathvariant="normal">Ξ</fc:mi><fc:mo stretchy="false">(</fc:mo><fc:mn>2030</fc:mn><fc:mo stretchy="false">)</fc:mo><fc:mo stretchy="false">→</fc:mo><fc:mi>π</fc:mi><fc:mi>π</fc:mi><fc:mi mathvariant="normal">Ξ</fc:mi><fc:mo>,</fc:mo><fc:mi>π</fc:mi><fc:mover accent="true"><fc:mi>K</fc:mi><fc:mo stretchy="false">¯</fc:mo></fc:mover><fc:mi mathvariant="normal">Σ</fc:mi><fc:mo>,</fc:mo><fc:mi>π</fc:mi><fc:mover accent="true"><fc:mi>K</fc:mi><fc:mo stretchy="false">¯</fc:mo></fc:mover><fc:mi mathvariant="normal">Λ</fc:mi></fc:math>. The results indicate that both the total decay width and partial decay widths agree well with experimental values within the error margins. This supports that <sc:math xmlns:sc="http://www.w3.org/1998/Math/MathML" display="inline"><sc:mi mathvariant="normal">Ξ</sc:mi><sc:mo stretchy="false">(</sc:mo><sc:mn>2030</sc:mn><sc:mo stretchy="false">)</sc:mo></sc:math> is a molecule with spin-parity <xc:math xmlns:xc="http://www.w3.org/1998/Math/MathML" display="inline"><xc:msup><xc:mi>J</xc:mi><xc:mi>P</xc:mi></xc:msup><xc:mo>=</xc:mo><xc:mn>5</xc:mn><xc:mo>/</xc:mo><xc:msup><xc:mn>2</xc:mn><xc:mo>+</xc:mo></xc:msup></xc:math>, predominantly composed of <zc:math xmlns:zc="http://www.w3.org/1998/Math/MathML" display="inline"><zc:msup><zc:mover accent="true"><zc:mi>K</zc:mi><zc:mo stretchy="false">¯</zc:mo></zc:mover><zc:mo>*</zc:mo></zc:msup><zc:mi mathvariant="normal">Σ</zc:mi></zc:math>. Compared to the experimental central values, our results are slightly smaller, which suggests that <ed:math xmlns:ed="http://www.w3.org/1998/Math/MathML" display="inline"><ed:mi mathvariant="normal">Ξ</ed:mi><ed:mo stretchy="false">(</ed:mo><ed:mn>2030</ed:mn><ed:mo stretchy="false">)</ed:mo></ed:math> may contain additional components besides meson-baryon molecular components, such as three-quark structures. Published by the American Physical Society 2024