Understanding the low-lying Ωc structures from a coupled-channel perspective

We perform a systematic analysis of the low-lying <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="normal">Ω</a:mi><a:mi>c</a:mi></a:msub></a:math> structures in a coupled-channel approach. The couplings between meson-baryon channels, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi mathvariant="normal">Ξ</d:mi><d:mi>c</d:mi></d:msub><d:mover accent="true"><d:mi>K</d:mi><d:mo stretchy="false">¯</d:mo></d:mover></d:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msubsup><i:mi mathvariant="normal">Ξ</i:mi><i:mi>c</i:mi><i:mo>′</i:mo></i:msubsup><i:mover accent="true"><i:mi>K</i:mi><i:mo stretchy="false">¯</i:mo></i:mover></i:math>, <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msubsup><n:mi mathvariant="normal">Ξ</n:mi><n:mi>c</n:mi><n:mo>*</n:mo></n:msubsup><n:mover accent="true"><n:mi>K</n:mi><n:mo stretchy="false">¯</n:mo></n:mover></n:math>, <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi mathvariant="normal">Ω</s:mi><s:mi>c</s:mi></s:msub><s:mi>η</s:mi></s:math>, and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msubsup><v:mi mathvariant="normal">Ω</v:mi><v:mi>c</v:mi><v:mo>*</v:mo></v:msubsup><v:mi>η</v:mi></v:math>, and three-quark bare states <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi mathvariant="normal">Ω</y:mi><y:mi>c</y:mi></y:msub><y:mo stretchy="false">(</y:mo><y:mn>1</y:mn><y:msub><y:mi>P</y:mi><y:mi>λ</y:mi></y:msub><y:mo stretchy="false">)</y:mo></y:math> are considered. We predict a bound state <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:msub><db:mi mathvariant="normal">Ω</db:mi><db:mi>c</db:mi></db:msub><db:mo stretchy="false">(</db:mo><db:mn>2954</db:mn><db:mo stretchy="false">)</db:mo></db:math> below 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:mover accent="true"><ib:mi>K</ib:mi><ib:mo stretchy="false">¯</ib:mo></ib:mover></ib:math> threshold with <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mo stretchy="false">(</nb:mo><nb:msup><nb:mi>J</nb:mi><nb:mi>P</nb:mi></nb:msup><nb:mo>,</nb:mo><nb:mi>j</nb:mi><nb:mo stretchy="false">)</nb:mo><nb:mo>=</nb:mo><nb:mo stretchy="false">(</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:mo>,</nb:mo><nb:mn>0</nb:mn><nb:mo stretchy="false">)</nb:mo></nb:math>, which can be studied in the final states of <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:msubsup><tb:mi mathvariant="normal">Ω</tb:mi><tb:mi>c</tb:mi><tb:mrow><tb:mo stretchy="false">(</tb:mo><tb:mo>*</tb:mo><tb:mo stretchy="false">)</tb:mo></tb:mrow></tb:msubsup><tb:mi>π</tb:mi></tb:math> and <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:msubsup><yb:mi mathvariant="normal">Ω</yb:mi><yb:mi>c</yb:mi><yb:mrow><yb:mo stretchy="false">(</yb:mo><yb:mo>*</yb:mo><yb:mo stretchy="false">)</yb:mo></yb:mrow></yb:msubsup><yb:mi>γ</yb:mi></yb:math>. Also, the resonances <dc:math xmlns:dc="http://www.w3.org/1998/Math/MathML" display="inline"><dc:msub><dc:mi mathvariant="normal">Ω</dc:mi><dc:mi>c</dc:mi></dc:msub><dc:mo stretchy="false">(</dc:mo><dc:mn>3000</dc:mn><dc:mo stretchy="false">)</dc:mo></dc:math> and <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:msub><ic:mi mathvariant="normal">Ω</ic:mi><ic:mi>c</ic:mi></ic:msub><ic:mo stretchy="false">(</ic:mo><ic:mn>3050</ic:mn><ic:mo stretchy="false">)</ic:mo></ic:math> can be classified as the lower <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"><nc:mo stretchy="false">(</nc:mo><nc:msup><nc:mi>J</nc:mi><nc:mi>P</nc:mi></nc:msup><nc:mo>,</nc:mo><nc:mi>j</nc:mi><nc:mo stretchy="false">)</nc:mo><nc:mo>=</nc:mo><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>1</nc:mn><nc:mo stretchy="false">)</nc:mo></nc:math> and <tc:math xmlns:tc="http://www.w3.org/1998/Math/MathML" display="inline"><tc:mo stretchy="false">(</tc:mo><tc:msup><tc:mi>J</tc:mi><tc:mi>P</tc:mi></tc:msup><tc:mo>,</tc:mo><tc:mi>j</tc:mi><tc:mo stretchy="false">)</tc:mo><tc:mo>=</tc:mo><tc:mo stretchy="false">(</tc:mo><tc:mn>3</tc:mn><tc:mo>/</tc:mo><tc:msup><tc:mn>2</tc:mn><tc:mo>−</tc:mo></tc:msup><tc:mo>,</tc:mo><tc:mn>1</tc:mn><tc:mo stretchy="false">)</tc:mo></tc:math> states, respectively. Our present assignments based on this coupled-channel perspective are significantly different from those of the traditional three-quark picture and of the molecular scenario. The future BelleII and LHCb experiments can search for the bound state <zc:math xmlns:zc="http://www.w3.org/1998/Math/MathML" display="inline"><zc:msub><zc:mi mathvariant="normal">Ω</zc:mi><zc:mi>c</zc:mi></zc:msub><zc:mo stretchy="false">(</zc:mo><zc:mn>2954</zc:mn><zc:mo stretchy="false">)</zc:mo></zc:math> and measure the spin-parities of particles <ed:math xmlns:ed="http://www.w3.org/1998/Math/MathML" display="inline"><ed:msub><ed:mi mathvariant="normal">Ω</ed:mi><ed:mi>c</ed:mi></ed:msub><ed:mo stretchy="false">(</ed:mo><ed:mn>3000</ed:mn><ed:mo stretchy="false">)</ed:mo></ed:math> and <jd:math xmlns:jd="http://www.w3.org/1998/Math/MathML" display="inline"><jd:msub><jd:mi mathvariant="normal">Ω</jd:mi><jd:mi>c</jd:mi></jd:msub><jd:mo stretchy="false">(</jd:mo><jd:mn>3050</jd:mn><jd:mo stretchy="false">)</jd:mo></jd:math> to test our predictions.