Possible bound states of heavy baryonium and heavy dibaryon systems

In this work, we systematically study the heavy baryonium and heavy dibaryon systems using the Bethe-Salpeter equation in the ladder and instantaneous approximations for the kernel. Our results indicate that all the heavy baryonium systems, specifically <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="normal">Λ</a:mi><a:mi>Q</a:mi></a:msub><a:msub><a:mover accent="true"><a:mi mathvariant="normal">Λ</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mi>Q</a:mi></a:msub></a:math>, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi mathvariant="normal">Ξ</g:mi><g:mi>Q</g:mi></g:msub><g:msub><g:mover accent="true"><g:mi mathvariant="normal">Ξ</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mi>Q</g:mi></g:msub></g:math>, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi mathvariant="normal">Σ</m:mi><m:mi>Q</m:mi></m:msub><m:msub><m:mover accent="true"><m:mi mathvariant="normal">Σ</m:mi><m:mo stretchy="false">¯</m:mo></m:mover><m:mi>Q</m:mi></m:msub></m:math>, <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msubsup><s:mi mathvariant="normal">Ξ</s:mi><s:mi>Q</s:mi><s:mo>′</s:mo></s:msubsup><s:msubsup><s:mover accent="true"><s:mi mathvariant="normal">Ξ</s:mi><s:mo stretchy="false">¯</s:mo></s:mover><s:mi>Q</s:mi><s:mo>′</s:mo></s:msubsup></s:math>, and <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi mathvariant="normal">Ω</y:mi><y:mi>Q</y:mi></y:msub><y:msub><y:mover accent="true"><y:mi mathvariant="normal">Ω</y:mi><y:mo stretchy="false">¯</y:mo></y:mover><y:mi>Q</y:mi></y:msub></y:math> (<eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mrow><eb:mi>Q</eb:mi><eb:mo>=</eb:mo><eb:mi>c</eb:mi></eb:mrow></eb:math>, <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mrow><gb:mi>b</gb:mi></gb:mrow></gb:math>), can form bound states. Among the heavy dibaryon systems, only the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi mathvariant="normal">Ξ</ib:mi><ib:mi>Q</ib:mi></ib:msub><ib:msub><ib:mi mathvariant="normal">Ξ</ib:mi><ib:mi>Q</ib:mi></ib:msub></ib:math> system with <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>I</mb:mi><mb:mo>=</mb:mo><mb:mn>0</mb:mn></mb:math> and the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msub><ob:mi mathvariant="normal">Σ</ob:mi><ob:mi>Q</ob:mi></ob:msub><ob:msub><ob:mi mathvariant="normal">Σ</ob:mi><ob:mi>Q</ob:mi></ob:msub></ob:math> systems with <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mi>I</sb:mi><sb:mo>=</sb:mo><sb:mn>0</sb:mn></sb:math> and <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:mi>I</ub:mi><ub:mo>=</ub:mo><ub:mn>1</ub:mn></ub:math> can exist as bound states. Additionally, the <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:msub><wb:mi mathvariant="normal">Σ</wb:mi><wb:mi>Q</wb:mi></wb:msub><wb:msub><wb:mover accent="true"><wb:mi mathvariant="normal">Σ</wb:mi><wb:mo stretchy="false">¯</wb:mo></wb:mover><wb:mi>Q</wb:mi></wb:msub></wb:math> system with <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:mi>I</cc:mi><cc:mo>=</cc:mo><cc:mn>2</cc:mn></cc:math> and the <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:msub><ec:mi mathvariant="normal">Σ</ec:mi><ec:mi>Q</ec:mi></ec:msub><ec:msub><ec:mi mathvariant="normal">Σ</ec:mi><ec:mi>Q</ec:mi></ec:msub></ec:math> system with <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:mi>I</ic:mi><ic:mo>=</ic:mo><ic:mn>1</ic:mn></ic:math> are not deeply bound. Published by the American Physical Society 2024