Triple-strangeness hidden-charm pentaquarks

We investigate the possible existence of triple-strangeness hidden-charm pentaquark states in the off-shell coupled-channel formalism. The open-charm meson-baryon <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mover accent="true"> <a:mi>D</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mi>s</a:mi> </a:msub> <a:msub> <a:mi mathvariant="normal">Ω</a:mi> <a:mi>c</a:mi> </a:msub> </a:math> , <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msub> <f:mover accent="true"> <f:mi>D</f:mi> <f:mo stretchy="false">¯</f:mo> </f:mover> <f:mi>s</f:mi> </f:msub> <f:msubsup> <f:mi mathvariant="normal">Ω</f:mi> <f:mi>c</f:mi> <f:mo>*</f:mo> </f:msubsup> </f:math> , <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msubsup> <k:mover accent="true"> <k:mi>D</k:mi> <k:mo stretchy="false">¯</k:mo> </k:mover> <k:mi>s</k:mi> <k:mo>*</k:mo> </k:msubsup> <k:msub> <k:mi mathvariant="normal">Ω</k:mi> <k:mi>c</k:mi> </k:msub> </k:math> , and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msubsup> <p:mover accent="true"> <p:mi>D</p:mi> <p:mo stretchy="false">¯</p:mo> </p:mover> <p:mi>s</p:mi> <p:mo>*</p:mo> </p:msubsup> <p:msubsup> <p:mi mathvariant="normal">Ω</p:mi> <p:mi>c</p:mi> <p:mo>*</p:mo> </p:msubsup> </p:math> channels are considered, together with the hidden-charm <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>J</u:mi> <u:mo>/</u:mo> <u:mi>ψ</u:mi> <u:mi mathvariant="normal">Ω</u:mi> </u:math> channel. The two-body kernel Feynman amplitudes are constructed from an effective Lagrangian based on hidden local symmetry and heavy-quark spin symmetry. The coupled Blankenbecler-Sugar equation is solved in the partial-wave helicity basis. We observe two triple-strangeness hidden-charm pentaquark states: <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mi>P</x:mi> <x:mrow> <x:mi>c</x:mi> <x:mover accent="true"> <x:mi>c</x:mi> <x:mo stretchy="false">¯</x:mo> </x:mover> <x:mi>s</x:mi> <x:mi>s</x:mi> <x:mi>s</x:mi> </x:mrow> </x:msub> <x:mo stretchy="false">(</x:mo> <x:mn>4787</x:mn> <x:mo stretchy="false">)</x:mo> </x:math> and <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:msub> <db:mi>P</db:mi> <db:mrow> <db:mi>c</db:mi> <db:mover accent="true"> <db:mi>c</db:mi> <db:mo stretchy="false">¯</db:mo> </db:mover> <db:mi>s</db:mi> <db:mi>s</db:mi> <db:mi>s</db:mi> </db:mrow> </db:msub> <db:mo stretchy="false">(</db:mo> <db:mn>4841</db:mn> <db:mo stretchy="false">)</db:mo> </db:math> , both with <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:msup> <jb:mi>J</jb:mi> <jb:mi>P</jb:mi> </jb:msup> <jb:mo>=</jb:mo> <jb:mn>1</jb:mn> <jb:mo>/</jb:mo> <jb:msup> <jb:mn>2</jb:mn> <jb:mo>−</jb:mo> </jb:msup> </jb:math> . The <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:msub> <lb:mi>P</lb:mi> <lb:mrow> <lb:mi>c</lb:mi> <lb:mover accent="true"> <lb:mi>c</lb:mi> <lb:mo stretchy="false">¯</lb:mo> </lb:mover> <lb:mi>s</lb:mi> <lb:mi>s</lb:mi> <lb:mi>s</lb:mi> </lb:mrow> </lb:msub> <lb:mo stretchy="false">(</lb:mo> <lb:mn>4787</lb:mn> <lb:mo stretchy="false">)</lb:mo> </lb:math> couples dominantly to the <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"> <rb:msubsup> <rb:mover accent="true"> <rb:mi>D</rb:mi> <rb:mo stretchy="false">¯</rb:mo> </rb:mover> <rb:mi>s</rb:mi> <rb:mo>*</rb:mo> </rb:msubsup> <rb:msub> <rb:mi mathvariant="normal">Ω</rb:mi> <rb:mi>c</rb:mi> </rb:msub> </rb:math> and <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"> <wb:msubsup> <wb:mover accent="true"> <wb:mi>D</wb:mi> <wb:mo stretchy="false">¯</wb:mo> </wb:mover> <wb:mi>s</wb:mi> <wb:mo>*</wb:mo> </wb:msubsup> <wb:msubsup> <wb:mi mathvariant="normal">Ω</wb:mi> <wb:mi>c</wb:mi> <wb:mo>*</wb:mo> </wb:msubsup> </wb:math> channels, while the <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"> <bc:msub> <bc:mi>P</bc:mi> <bc:mrow> <bc:mi>c</bc:mi> <bc:mover accent="true"> <bc:mi>c</bc:mi> <bc:mo stretchy="false">¯</bc:mo> </bc:mover> <bc:mi>s</bc:mi> <bc:mi>s</bc:mi> <bc:mi>s</bc:mi> </bc:mrow> </bc:msub> <bc:mo stretchy="false">(</bc:mo> <bc:mn>4841</bc:mn> <bc:mo stretchy="false">)</bc:mo> </bc:math> couples almost exclusively to the <hc:math xmlns:hc="http://www.w3.org/1998/Math/MathML" display="inline"> <hc:msubsup> <hc:mover accent="true"> <hc:mi>D</hc:mi> <hc:mo stretchy="false">¯</hc:mo> </hc:mover> <hc:mi>s</hc:mi> <hc:mo>*</hc:mo> </hc:msubsup> <hc:msubsup> <hc:mi mathvariant="normal">Ω</hc:mi> <hc:mi>c</hc:mi> <hc:mo>*</hc:mo> </hc:msubsup> </hc:math> channel. The total transition cross sections of <mc:math xmlns:mc="http://www.w3.org/1998/Math/MathML" display="inline"> <mc:msubsup> <mc:mover accent="true"> <mc:mi>D</mc:mi> <mc:mo stretchy="false">¯</mc:mo> </mc:mover> <mc:mi>s</mc:mi> <mc:mrow> <mc:mo stretchy="false">(</mc:mo> <mc:mo>*</mc:mo>