Prediction of QQqqs¯ molecular pentaquarks within the extended local hidden gauge approach

We investigate hadronic molecular states with the quark contents <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>c</a:mi><a:mi>c</a:mi><a:mi>q</a:mi><a:mi>q</a:mi><a:mover accent="true"><a:mi>s</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math>, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>b</e:mi><e:mi>b</e:mi><e:mi>q</e:mi><e:mi>q</e:mi><e:mover accent="true"><e:mi>s</e:mi><e:mo stretchy="false">¯</e:mo></e:mover></e:math>, and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>b</i:mi><i:mi>c</i:mi><i:mi>q</i:mi><i:mi>q</i:mi><i:mover accent="true"><i:mi>s</i:mi><i:mo stretchy="false">¯</i:mo></i:mover></i:math> (<m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mi>q</m:mi><m:mo>=</m:mo><m:mi>u</m:mi></m:mrow></m:math>, <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:mi>d</o:mi></o:mrow></o:math>) by employing the extended local hidden gauge approach. Considering that the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>S</q:mi></q:math>-wave meson-baryon interactions are dominated by vector meson exchange, the coupled channels scattering amplitudes are obtained by solving the Bethe-Salpeter equation in its on-shell form. We find that the poles appearing on the complex Riemann sheet are potential candidates for dynamically generated molecular pentaquark states. The results suggest the existence of a total of fourteen molecular states with quantum numbers <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>I</s:mi><s:mo stretchy="false">(</s:mo><s:msup><s:mi>J</s:mi><s:mi>P</s:mi></s:msup><s:mo stretchy="false">)</s:mo><s:mo>=</s:mo><s:mn>0</s:mn><s:mo stretchy="false">(</s:mo><s:mn>1</s:mn><s:mo>/</s:mo><s:msup><s:mn>2</s:mn><s:mo>−</s:mo></s:msup><s:mo stretchy="false">)</s:mo></s:math>, <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mn>0</y:mn><y:mo stretchy="false">(</y:mo><y:mn>3</y:mn><y:mo>/</y:mo><y:msup><y:mn>2</y:mn><y:mo>−</y:mo></y:msup><y:mo stretchy="false">)</y:mo></y:math>, and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mn>0</cb:mn><cb:mo stretchy="false">(</cb:mo><cb:mn>5</cb:mn><cb:mo>/</cb:mo><cb:msup><cb:mn>2</cb:mn><cb:mo>−</cb:mo></cb:msup><cb:mo stretchy="false">)</cb:mo></cb:math>, which arise from the interactions of the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msup><gb:mi>K</gb:mi><gb:mrow><gb:mo stretchy="false">(</gb:mo><gb:mo>*</gb:mo><gb:mo stretchy="false">)</gb:mo></gb:mrow></gb:msup><gb:msubsup><gb:mi mathvariant="normal">Ξ</gb:mi><gb:mrow><gb:mi>c</gb:mi><gb:mi>c</gb:mi></gb:mrow><gb:mrow><gb:mo stretchy="false">(</gb:mo><gb:mo>*</gb:mo><gb:mo stretchy="false">)</gb:mo></gb:mrow></gb:msubsup></gb:math>, <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:msup><nb:mi>K</nb:mi><nb:mrow><nb:mo stretchy="false">(</nb:mo><nb:mo>*</nb:mo><nb:mo stretchy="false">)</nb:mo></nb:mrow></nb:msup><nb:msubsup><nb:mi mathvariant="normal">Ξ</nb:mi><nb:mrow><nb:mi>b</nb:mi><nb:mi>b</nb:mi></nb:mrow><nb:mrow><nb:mo stretchy="false">(</nb:mo><nb:mo>*</nb:mo><nb:mo stretchy="false">)</nb:mo></nb:mrow></nb:msubsup></nb:math>, <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:msup><ub:mi>K</ub:mi><ub:mrow><ub:mo stretchy="false">(</ub:mo><ub:mo>*</ub:mo><ub:mo stretchy="false">)</ub:mo></ub:mrow></ub:msup><ub:msubsup><ub:mi mathvariant="normal">Ξ</ub:mi><ub:mrow><ub:mi>b</ub:mi><ub:mi>c</ub:mi></ub:mrow><ub:mrow><ub:mo stretchy="false">(</ub:mo><ub:mo>*</ub:mo><ub:mo stretchy="false">)</ub:mo></ub:mrow></ub:msubsup></ub:math>, and <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:msup><bc:mi>K</bc:mi><bc:mrow><bc:mo stretchy="false">(</bc:mo><bc:mo>*</bc:mo><bc:mo stretchy="false">)</bc:mo></bc:mrow></bc:msup><bc:msubsup><bc:mi mathvariant="normal">Ξ</bc:mi><bc:mrow><bc:mi>b</bc:mi><bc:mi>c</bc:mi></bc:mrow><bc:mo>′</bc:mo></bc:msubsup></bc:math> channels, respectively. Their binding energies are calculated to be about 0.1–33 MeV, and this range depends on the free parameter of the theory. Our research contributes to the spectroscopic studies of hadronic molecular pentaquark states.