Masses and decay widths of the S -wave ΛcΛ¯c bound states

In this work, we investigate possible bound states of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="normal">Λ</a:mi><a:mi>c</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>c</a:mi></a:msub></a:math> system in the Bethe-Salpeter formalism in the ladder and instantaneous approximations. By numerically solving the Bethe-Salpeter equation, we confirm the existence of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi mathvariant="normal">Λ</g:mi><g:mi>c</g:mi></g:msub><g:msub><g:mover accent="true"><g:mi mathvariant="normal">Λ</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mi>c</g:mi></g:msub></g:math> bound states with quantum numbers <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>J</m:mi><m:mrow><m:mi>P</m:mi><m:mi>C</m:mi></m:mrow></m:msup><m:mo>=</m:mo><m:msup><m:mn>0</m:mn><m:mrow><m:mo>−</m:mo><m:mo>+</m:mo></m:mrow></m:msup></m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>J</o:mi><o:mrow><o:mi>P</o:mi><o:mi>C</o:mi></o:mrow></o:msup><o:mo>=</o:mo><o:msup><o:mn>1</o:mn><o:mrow><o:mo>−</o:mo><o:mo>−</o:mo></o:mrow></o:msup></o:math>. We further investigate the partial decay widths of the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi mathvariant="normal">Λ</q:mi><q:mi>c</q:mi></q:msub><q:msub><q:mover accent="true"><q:mi mathvariant="normal">Λ</q:mi><q:mo stretchy="false">¯</q:mo></q:mover><q:mi>c</q:mi></q:msub></q:math> bound states into <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>N</w:mi><w:mover accent="true"><w:mi>N</w:mi><w:mo stretchy="false">¯</w:mo></w:mover></w:math>, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>D</ab:mi><ab:mover accent="true"><ab:mi>D</ab:mi><ab:mo stretchy="false">¯</ab:mo></ab:mover></ab:math>, <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>D</eb:mi><eb:msup><eb:mover accent="true"><eb:mi>D</eb:mi><eb:mo stretchy="false">¯</eb:mo></eb:mover><eb:mo>*</eb:mo></eb:msup></eb:math>, <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msup><ib:mi>D</ib:mi><ib:mo>*</ib:mo></ib:msup><ib:msup><ib:mover accent="true"><ib:mi>D</ib:mi><ib:mo stretchy="false">¯</ib:mo></ib:mover><ib:mo>*</ib:mo></ib:msup></ib:math>, <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>π</mb:mi><mb:mover accent="true"><mb:mi>π</mb:mi><mb:mo stretchy="false">¯</mb:mo></mb:mover></mb:math>, and <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mi>K</qb:mi><qb:mover accent="true"><qb:mi>K</qb:mi><qb:mo stretchy="false">¯</qb:mo></qb:mover></qb:math>. Our results indicate that the decay width of the <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:msub><ub:mi mathvariant="normal">Λ</ub:mi><ub:mi>c</ub:mi></ub:msub><ub:msub><ub:mover accent="true"><ub:mi mathvariant="normal">Λ</ub:mi><ub:mo stretchy="false">¯</ub:mo></ub:mover><ub:mi>c</ub:mi></ub:msub></ub:math> bound state with <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:msup><ac:mi>J</ac:mi><ac:mrow><ac:mi>P</ac:mi><ac:mi>C</ac:mi></ac:mrow></ac:msup><ac:mo>=</ac:mo><ac:msup><ac:mn>1</ac:mn><ac:mrow><ac:mo>−</ac:mo><ac:mo>−</ac:mo></ac:mrow></ac:msup></ac:math> is much larger than that with <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:msup><cc:mi>J</cc:mi><cc:mrow><cc:mi>P</cc:mi><cc:mi>C</cc:mi></cc:mrow></cc:msup><cc:mo>=</cc:mo><cc:msup><cc:mn>0</cc:mn><cc:mrow><cc:mo>−</cc:mo><cc:mo>+</cc:mo></cc:mrow></cc:msup></cc:math>, and among their decay channels, the <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:mi>D</ec:mi><ec:msup><ec:mover accent="true"><ec:mi>D</ec:mi><ec:mo stretchy="false">¯</ec:mo></ec:mover><ec:mo>*</ec:mo></ec:msup></ec:math> final state is the main decay mode. We suggest experiments to search for the <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:msub><ic:mi mathvariant="normal">Λ</ic:mi><ic:mi>c</ic:mi></ic:msub><ic:msub><ic:mover accent="true"><ic:mi mathvariant="normal">Λ</ic:mi><ic:mo stretchy="false">¯</ic:mo></ic:mover><ic:mi>c</ic:mi></ic:msub></ic:math> bound states in the <oc:math xmlns:oc="http://www.w3.org/1998/Math/MathML" display="inline"><oc:mi>D</oc:mi><oc:msup><oc:mover accent="true"><oc:mi>D</oc:mi><oc:mo stretchy="false">¯</oc:mo></oc:mover><oc:mo>*</oc:mo></oc:msup></oc:math> final state.