Structure of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mn>2012</mml:mn><mml:mo stretchy="false">

We investigate the internal structure of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Ω</a:mi><a:mo stretchy="false">(</a:mo><a:mn>2012</a:mn><a:msup><a:mo stretchy="false">)</a:mo><a:mo>−</a:mo></a:msup></a:math> by analyzing lattice QCD simulation and experimental data within Hamiltonian effective field theory, considering both <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msup><f:mi>J</f:mi><f:mi>P</f:mi></f:msup><f:mo>=</f:mo><f:mn>1</f:mn><f:mo>/</f:mo><f:msup><f:mn>2</f:mn><f:mo>−</f:mo></f:msup></f:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mn>3</h:mn><h:mo>/</h:mo><h:msup><h:mn>2</h:mn><h:mo>−</h:mo></h:msup></h:math> assignments. The couplings to the dominant decay channel <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi mathvariant="normal">Ξ</j:mi><j:mover accent="true"><j:mi>K</j:mi><j:mo stretchy="false">¯</j:mo></j:mover></j:math> and the near-threshold channel <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi mathvariant="normal">Ξ</o:mi><o:mo stretchy="false">(</o:mo><o:mn>1530</o:mn><o:mo stretchy="false">)</o:mo><o:mover accent="true"><o:mi>K</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math> are determined through the quark-pair-creation model. By studying the lattice QCD spectra in these two spin-parity scenarios, we extract the masses and widths of the resonances. We notice that the <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msup><v:mi>J</v:mi><v:mi>P</v:mi></v:msup><v:mo>=</v:mo><v:mn>3</v:mn><v:mo>/</v:mo><v:msup><v:mn>2</v:mn><v:mo>−</v:mo></v:msup></v:math> resonance is consistent with the observed <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi mathvariant="normal">Ω</x:mi><x:mo stretchy="false">(</x:mo><x:mn>2012</x:mn><x:msup><x:mo stretchy="false">)</x:mo><x:mo>−</x:mo></x:msup></x:math> while the recently reported <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi mathvariant="normal">Ω</cb:mi><cb:mo stretchy="false">(</cb:mo><cb:mn>2109</cb:mn><cb:msup><cb:mo stretchy="false">)</cb:mo><cb:mo>−</cb:mo></cb:msup></cb:math> may be a <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msup><hb:mi>J</hb:mi><hb:mi>P</hb:mi></hb:msup><hb:mo>=</hb:mo><hb:mn>1</hb:mn><hb:mo>/</hb:mo><hb:msup><hb:mn>2</hb:mn><hb:mo>−</hb:mo></hb:msup></hb:math> <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mi mathvariant="normal">Ω</jb:mi></jb:math>.