Investigation on the Ω(2012) from QCD sum rules

We study the recently observed <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:math> baryon in quantum chromodynamics (QCD) sum rules. We construct the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>P</f:mi></f:math>-wave <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi mathvariant="normal">Ω</h:mi></h:math> baryon currents with a covariant derivative, and perform spin projection to obtain the currents with total spin <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mn>1</k:mn><k:mo>/</k:mo><k:mn>2</k:mn></k:mrow></k:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mn>3</m:mn><m:mo>/</m:mo><m:mn>2</m:mn></m:mrow></m:math>. We then apply the parity-projected QCD sum rules to separate the contributions of the positive and negative parity states. We extract the masses of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:msup><o:mrow><o:mi>J</o:mi></o:mrow><o:mrow><o:mi>P</o:mi></o:mrow></o:msup><o:mo>=</o:mo><o:mn>1</o:mn><o:mo>/</o:mo><o:msup><o:mrow><o:mn>2</o:mn></o:mrow><o:mrow><o:mo>−</o:mo></o:mrow></o:msup></o:mrow></o:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mn>3</q:mn><q:mo>/</q:mo><q:msup><q:mn>2</q:mn><q:mo>−</q:mo></q:msup></q:math> states to be <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:msub><s:mrow><s:mi>M</s:mi></s:mrow><s:mrow><s:mn>1</s:mn><s:mo>/</s:mo><s:msup><s:mrow><s:mn>2</s:mn></s:mrow><s:mrow><s:mo>−</s:mo></s:mrow></s:msup></s:mrow></s:msub><s:mo>=</s:mo><s:msubsup><s:mrow><s:mn>2.07</s:mn></s:mrow><s:mrow><s:mo>−</s:mo><s:mn>0.07</s:mn></s:mrow><s:mrow><s:mo>+</s:mo><s:mn>0.07</s:mn></s:mrow></s:msubsup><s:mtext> </s:mtext><s:mtext> </s:mtext><s:mi>GeV</s:mi></s:mrow></s:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:msub><u:mrow><u:mi>M</u:mi></u:mrow><u:mrow><u:mn>3</u:mn><u:mo>/</u:mo><u:msup><u:mrow><u:mn>2</u:mn></u:mrow><u:mrow><u:mo>−</u:mo></u:mrow></u:msup></u:mrow></u:msub><u:mo>=</u:mo><u:msubsup><u:mrow><u:mn>2.05</u:mn></u:mrow><u:mrow><u:mo>−</u:mo><u:mn>0.10</u:mn></u:mrow><u:mrow><u:mo>+</u:mo><u:mn>0.09</u:mn></u:mrow></u:msubsup><u:mtext> </u:mtext><u:mtext> </u:mtext><u:mi>GeV</u:mi></u:mrow></u:math>. Both results are in good agreement with the experimental result. Therefore, it is likely that the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi mathvariant="normal">Ω</w:mi><w:mo stretchy="false">(</w:mo><w:mn>2012</w:mn><w:mo stretchy="false">)</w:mo></w:math> is a negative parity state, which is interpreted as a <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mi>P</bb:mi></bb:math>-wave excited state in the quark model. However, its spin is not determined in the present analysis, which can be done by detailed study on its decay properties. Published by the American Physical Society 2024