2P -wave charmed baryons from QCD sum rules

We conduct an investigation on the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>1</a:mn><a:mi>P</a:mi></a:math>- and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>2</c:mn><c:mi>P</c:mi></c:math>-wave charmed baryons using the methods of QCD sum rules and light-cone sum rules within the framework of heavy quark effective theory. Our results suggest that the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi mathvariant="normal">Λ</e:mi><e:mi>c</e:mi></e:msub><e:mo stretchy="false">(</e:mo><e:mn>2910</e:mn><e:msup><e:mo stretchy="false">)</e:mo><e:mo>+</e:mo></e:msup></e:math>, <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi mathvariant="normal">Λ</j:mi><j:mi>c</j:mi></j:msub><j:mo stretchy="false">(</j:mo><j:mn>2940</j:mn><j:msup><j:mo stretchy="false">)</j:mo><j:mo>+</j:mo></j:msup></j:math>, and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi mathvariant="normal">Ξ</o:mi><o:mi>c</o:mi></o:msub><o:mo stretchy="false">(</o:mo><o:mn>3123</o:mn><o:msup><o:mo stretchy="false">)</o:mo><o:mo>+</o:mo></o:msup></o:math> can be well interpreted as the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mn>2</t:mn><t:mi>P</t:mi></t:math>-wave charmed baryons of <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>1</v:mn><v:mo>/</v:mo><v:msup><v:mn>2</v:mn><v:mo>−</v:mo></v:msup></v:math> and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mn>3</x:mn><x:mo>/</x:mo><x:msup><x:mn>2</x:mn><x:mo>−</x:mo></x:msup></x:math>, belonging to the <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi>S</z:mi><z:mi>U</z:mi><z:mo stretchy="false">(</z:mo><z:mn>3</z:mn><z:mo stretchy="false">)</z:mo></z:math> flavor <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:msub><db:mover accent="true"><db:mn mathvariant="bold">3</db:mn><db:mo stretchy="false">¯</db:mo></db:mover><db:mi>F</db:mi></db:msub></db:math> representation. Moreover, the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi mathvariant="normal">Ξ</ib:mi><ib:mi>c</ib:mi></ib:msub><ib:mo stretchy="false">(</ib:mo><ib:mn>3123</ib:mn><ib:msup><ib:mo stretchy="false">)</ib:mo><ib:mo>+</ib:mo></ib:msup></ib:math> possesses a partner state characterized by <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:msup><nb:mi>J</nb:mi><nb:mi>P</nb:mi></nb:msup><nb:mo>=</nb:mo><nb:mn>1</nb:mn><nb:mo>/</nb:mo><nb:msup><nb:mn>2</nb:mn><nb:mo>−</nb:mo></nb:msup></nb:math>, denoted as <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:msub><pb:mi mathvariant="normal">Ξ</pb:mi><pb:mi>c</pb:mi></pb:msub><pb:mo stretchy="false">(</pb:mo><pb:mn>1</pb:mn><pb:mo>/</pb:mo><pb:msup><pb:mn>2</pb:mn><pb:mo>−</pb:mo></pb:msup><pb:mo>,</pb:mo><pb:mn>2</pb:mn><pb:mi>P</pb:mi><pb:mo stretchy="false">)</pb:mo></pb:math>. Our analysis predicts its mass and width to be <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:msub><ub:mi>m</ub:mi><ub:mrow><ub:msub><ub:mi mathvariant="normal">Ξ</ub:mi><ub:mi>c</ub:mi></ub:msub><ub:mo stretchy="false">(</ub:mo><ub:mn>1</ub:mn><ub:mo>/</ub:mo><ub:msup><ub:mn>2</ub:mn><ub:mo>−</ub:mo></ub:msup><ub:mo>,</ub:mo><ub:mn>2</ub:mn><ub:mi>P</ub:mi><ub:mo stretchy="false">)</ub:mo></ub:mrow></ub:msub><ub:mo>−</ub:mo><ub:msub><ub:mi>m</ub:mi><ub:mrow><ub:msub><ub:mi mathvariant="normal">Ξ</ub:mi><ub:mi>c</ub:mi></ub:msub><ub:mo stretchy="false">(</ub:mo><ub:mn>3123</ub:mn><ub:msup><ub:mo stretchy="false">)</ub:mo><ub:mo>+</ub:mo></ub:msup></ub:mrow></ub:msub><ub:mo>=</ub:mo><ub:mo>−</ub:mo><ub:mn>18</ub:mn><ub:mo>±</ub:mo><ub:mn>7</ub:mn><ub:mtext> </ub:mtext><ub:mtext> </ub:mtext><ub:mi>MeV</ub:mi></ub:math> and <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:msub><cc:mi mathvariant="normal">Γ</cc:mi><cc:mrow><cc:msub><cc:mi mathvariant="normal">Ξ</cc:mi><cc:mi>c</cc:mi></cc:msub><cc:mo stretchy="false">(</cc:mo><cc:mn>2</cc:mn><cc:mi>P</cc:mi><cc:mo>,</cc:mo><cc:mn>1</cc:mn><cc:mo>/</cc:mo><cc:msup><cc:mn>2</cc:mn><cc:mo>−</cc:mo></cc:msup><cc:mo stretchy="false">)</cc:mo></cc:mrow></cc:msub><cc:mo>=</cc:mo><cc:mn>3</cc:mn><cc:msubsup><cc:mn>1</cc:mn><cc:mrow><cc:mo>−</cc:mo><cc:mn>27</cc:mn></cc:mrow><cc:mrow><cc:mo>+</cc:mo><cc:mn>170</cc:mn></cc:mrow></cc:msubsup><cc:mtext> </cc:mtext><cc:mtext> </cc:mtext><cc:mi>MeV</cc:mi></cc:math>, with <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:msub><ic:mi>m</ic:mi><ic:mrow><ic:msub><ic:mi mathvariant="normal">Ξ</ic:mi><ic:mi>c</ic:mi></ic:msub><ic:mo stretchy="false">(</ic:mo><ic:mn>3123</ic:mn><ic:msup><ic:mo stretchy="false">)</ic:mo><ic:mo>+</ic:mo></ic:msup></ic:mrow></ic:msub><ic:mo>=</ic:mo><ic:mn>3122.9</ic:mn><ic:mo>±</ic:mo><ic:mn>1.3</ic:mn><ic:mtext> </ic:mtext><ic:mtext> </ic:mtext><ic:mi>MeV</ic:mi></ic:math>. We propose to search for it in the <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"><nc:msub><nc:mi mathvariant="normal">Ξ</nc:mi><nc:mi>c</nc:mi></nc:msub><nc:mo stretchy="false">(</nc:mo><nc:mn>1</nc:mn><nc:mo>/</nc:mo><nc:msup><nc:mn>2</nc:mn><nc:mo>−</nc:mo></nc:msup><nc:mo>,</nc:mo><nc:mn>2</nc:mn><nc:mi>P</nc:mi><nc:mo stretchy="false">)</nc:mo><nc:mo stretchy="false">→</nc:mo><nc:msub><nc:mi mathvariant="normal">Σ</nc:mi><nc:mi>c</nc:mi></nc:msub><nc:mi>K</nc:mi></nc:math> decay channel. Published by the American Physical Society 2024