Double-strangeness hidden-charm pentaquarks

We investigate the possible existence of double-strangeness hidden-charm pentaquark states, denoted as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>P</a:mi></a:mrow><a:mrow><a:mi>c</a:mi><a:mover accent="true"><a:mrow><a:mi>c</a:mi></a:mrow><a:mrow><a:mo stretchy="false">¯</a:mo></a:mrow></a:mover><a:mi>s</a:mi><a:mi>s</a:mi></a:mrow></a:msub></a:mrow></a:math>, within an off-shell coupled-channel formalism. Eleven meson–baryon channels with total strangeness <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>S</e:mi><e:mo>=</e:mo><e:mo>−</e:mo><e:mn>2</e:mn></e:math> are constructed by combining charmed mesons and singly charmed baryons. The two-body scattering amplitudes are derived from an effective Lagrangian that respects heavy-quark spin symmetry, hidden local symmetry, and flavor SU(3) symmetry. The Bethe-Salpeter equation is solved using the Blankenbecler-Sugar reduction scheme, and resonances are identified as poles in the scattering amplitudes on the complex energy plane. We find five negative-parity <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>P</g:mi><g:mrow><g:mi>c</g:mi><g:mover accent="true"><g:mi>c</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mi>s</g:mi><g:mi>s</g:mi></g:mrow></g:msub></g:math> states with spins <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>J</k:mi><k:mo>=</k:mo><k:mn>1</k:mn><k:mo>/</k:mo><k:mn>2</k:mn></k:math>, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mn>3</m:mn><m:mo>/</m:mo><m:mn>2</m:mn></m:math>, and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mn>5</o:mn><o:mo>/</o:mo><o:mn>2</o:mn></o:math>, all located below their relevant thresholds. Three positive-parity states are also found: two with <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>J</q:mi><q:mo>=</q:mo><q:mn>1</q:mn><q:mo>/</q:mo><q:mn>2</q:mn></q:math> and one with <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>J</s:mi><s:mo>=</s:mo><s:mn>3</s:mn><s:mo>/</s:mo><s:mn>2</s:mn></s:math>, lying above the thresholds with substantial widths. The coupling strengths of each resonance to relevant meson-baryon channels are extracted. The sensitivity of the results to the cutoff parameter <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi mathvariant="normal">Λ</u:mi><u:mn>0</u:mn></u:msub><u:mo>=</u:mo><u:mi mathvariant="normal">Λ</u:mi><u:mo>−</u:mo><u:mi>m</u:mi></u:math> is examined. These results provide theoretical predictions that may assist future experimental searches for <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>P</y:mi><y:mrow><y:mi>c</y:mi><y:mover accent="true"><y:mi>c</y:mi><y:mo stretchy="false">¯</y:mo></y:mover><y:mi>s</y:mi><y:mi>s</y:mi></y:mrow></y:msub></y:math> states in the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>J</cb:mi><cb:mo>/</cb:mo><cb:mi>ψ</cb:mi><cb:mi mathvariant="normal">Ξ</cb:mi></cb:math> channel.