Radiative decays of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Ω</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2012</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> as a

We present a theoretical investigation of the radiative decay process <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:mo stretchy="false">)</a:mo> <a:mo stretchy="false">→</a:mo> <a:mi>γ</a:mi> <a:mi mathvariant="normal">Ω</a:mi> </a:math> , where the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi mathvariant="normal">Ω</h:mi> <h:mo stretchy="false">(</h:mo> <h:mn>2012</h:mn> <h:mo stretchy="false">)</h:mo> </h:math> resonance with spin-parity <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msup> <m:mi>J</m:mi> <m:mi>P</m:mi> </m:msup> <m:mo>=</m:mo> <m:msup> <m:mfrac> <m:mn>3</m:mn> <m:mn>2</m:mn> </m:mfrac> <m:mo>−</m:mo> </m:msup> </m:math> is treated as a dynamically generated state from <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mover accent="true"> <o:mi>K</o:mi> <o:mo stretchy="false">¯</o:mo> </o:mover> <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:math> and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mi>η</v:mi> <v:mi mathvariant="normal">Ω</v:mi> </v:math> in <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>s</y:mi> </y:math> -wave and <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mover accent="true"> <ab:mi>K</ab:mi> <ab:mo stretchy="false">¯</ab:mo> </ab:mover> <ab:mi mathvariant="normal">Ξ</ab:mi> </ab:math> in <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mi>d</fb:mi> </fb:math> -wave. The radiative decay width of the <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:mi mathvariant="normal">Ω</hb:mi> <hb:mo stretchy="false">(</hb:mo> <hb:mn>2012</hb:mn> <hb:mo stretchy="false">)</hb:mo> </hb:math> is calculated using a triangular loop mechanism, where the <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mi mathvariant="normal">Ω</mb:mi> <mb:mo stretchy="false">(</mb:mo> <mb:mn>2012</mb:mn> <mb:mo stretchy="false">)</mb:mo> </mb:math> couples to the <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"> <rb:mover accent="true"> <rb:mi>K</rb:mi> <rb:mo stretchy="false">¯</rb:mo> </rb:mover> <rb:mi mathvariant="normal">Ξ</rb:mi> <rb:mo stretchy="false">(</rb:mo> <rb:mn>1530</rb:mn> <rb:mo stretchy="false">)</rb:mo> </rb:math> channel. Subsequently, the final-state interactions between <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:mi mathvariant="normal">Ξ</yb:mi> <yb:mo stretchy="false">(</yb:mo> <yb:mn>1530</yb:mn> <yb:mo stretchy="false">)</yb:mo> </yb:math> and <dc:math xmlns:dc="http://www.w3.org/1998/Math/MathML" display="inline"> <dc:mover accent="true"> <dc:mi>K</dc:mi> <dc:mo stretchy="false">¯</dc:mo> </dc:mover> </dc:math> transition to a photon and <hc:math xmlns:hc="http://www.w3.org/1998/Math/MathML" display="inline"> <hc:mi mathvariant="normal">Ω</hc:mi> </hc:math> through the exchange of a <kc:math xmlns:kc="http://www.w3.org/1998/Math/MathML" display="inline"> <kc:mi mathvariant="normal">Ξ</kc:mi> </kc:math> baryon. Our calculations yield a radiative decay width of <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"> <nc:mrow> <nc:msubsup> <nc:mrow> <nc:mn>13.2</nc:mn> </nc:mrow> <nc:mrow> <nc:mo>−</nc:mo> <nc:mn>5.6</nc:mn> </nc:mrow> <nc:mrow> <nc:mo>+</nc:mo> <nc:mn>4.5</nc:mn> </nc:mrow> </nc:msubsup> <nc:mtext> </nc:mtext> <nc:mtext> </nc:mtext> <nc:mi>keV</nc:mi> </nc:mrow> </nc:math> , with uncertainties arising from the model parameters. This result provides valuable insights into the nature of the <pc:math xmlns:pc="http://www.w3.org/1998/Math/MathML" display="inline"> <pc:mi mathvariant="normal">Ω</pc:mi> <pc:mo stretchy="false">(</pc:mo> <pc:mn>2012</pc:mn> <pc:mo stretchy="false">)</pc:mo> </pc:math> resonance and its decay dynamics. It is expected that the calculations presented here could be verified by future experiments, which would open a new door for studying the still elusive nature of Ω(2012).