Investigation of the mass spectra of singly heavy baryons ΣQ , ΞQ′ , and <mml:…

Very recently, LHCb Collaboration observed that two new <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi mathvariant="normal">Ω</a:mi><a:mi>c</a:mi><a:mn>0</a:mn></a:msubsup></a:math> states decay into <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msubsup><d:mi mathvariant="normal">Ξ</d:mi><d:mi>c</d:mi><d:mo>+</d:mo></d:msubsup><d:msup><d:mi>K</d:mi><d:mo>−</d:mo></d:msup></d:math> with masses of about 3185 MeV and 3327 MeV. However, their spin-parity quantum numbers <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>J</g:mi><g:mi>P</g:mi></g:msup></g:math> have not been determined. In this paper, we exploit the quark-diquark model, the linear Regge trajectory and the perturbation treatment method to analyze the mass spectra of the discovered experimental data for the singly heavy baryons <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi mathvariant="normal">Σ</i:mi><i:mi>c</i:mi></i:msub><i:mo>/</i:mo><i:msub><i:mi mathvariant="normal">Σ</i:mi><i:mi>b</i:mi></i:msub></i:math>, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msubsup><m:mi mathvariant="normal">Ξ</m:mi><m:mi>c</m:mi><m:mo>′</m:mo></m:msubsup><m:mo>/</m:mo><m:msubsup><m:mi mathvariant="normal">Ξ</m:mi><m:mi>b</m:mi><m:mo>′</m:mo></m:msubsup></m:math>, and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi mathvariant="normal">Ω</q:mi><q:mi>c</q:mi></q:msub><q:mo>/</q:mo><q:msub><q:mi mathvariant="normal">Ω</q:mi><q:mi>b</q:mi></q:msub></q:math>. In addition, we further predict the mass spectra of several unobserved <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi mathvariant="normal">Σ</u:mi><u:mi>c</u:mi></u:msub><u:mo>/</u:mo><u:msub><u:mi mathvariant="normal">Σ</u:mi><u:mi>b</u:mi></u:msub></u:math>, <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msubsup><y:mi mathvariant="normal">Ξ</y:mi><y:mi>c</y:mi><y:mo>′</y:mo></y:msubsup><y:mo>/</y:mo><y:msubsup><y:mi mathvariant="normal">Ξ</y:mi><y:mi>b</y:mi><y:mo>′</y:mo></y:msubsup></y:math>, and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi mathvariant="normal">Ω</cb:mi><cb:mi>c</cb:mi></cb:msub><cb:mo>/</cb:mo><cb:msub><cb:mi mathvariant="normal">Ω</cb:mi><cb:mi>b</cb:mi></cb:msub></cb:math> baryons. In the case of the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi mathvariant="normal">Ω</gb:mi><gb:mi>c</gb:mi></gb:msub><gb:mo stretchy="false">(</gb:mo><gb:mn>3185</gb:mn><gb:msup><gb:mo stretchy="false">)</gb:mo><gb:mn>0</gb:mn></gb:msup></gb:math> and <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:msub><lb:mi mathvariant="normal">Ω</lb:mi><lb:mi>c</lb:mi></lb:msub><lb:mo stretchy="false">(</lb:mo><lb:mn>3327</lb:mn><lb:msup><lb:mo stretchy="false">)</lb:mo><lb:mn>0</lb:mn></lb:msup></lb:math> states, we determine <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:msub><qb:mi mathvariant="normal">Ω</qb:mi><qb:mi>c</qb:mi></qb:msub><qb:mo stretchy="false">(</qb:mo><qb:mn>3185</qb:mn><qb:msup><qb:mo stretchy="false">)</qb:mo><qb:mn>0</qb:mn></qb:msup></qb:math> as <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:mn>2</vb:mn><vb:mi>S</vb:mi></vb:math> state and <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:msub><xb:mi mathvariant="normal">Ω</xb:mi><xb:mi>c</xb:mi></xb:msub><xb:mo stretchy="false">(</xb:mo><xb:mn>3327</xb:mn><xb:msup><xb:mo stretchy="false">)</xb:mo><xb:mn>0</xb:mn></xb:msup></xb:math> as <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:mn>1</cc:mn><cc:mi>D</cc:mi></cc:math> state with <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:msup><ec:mi>J</ec:mi><ec:mi>P</ec:mi></ec:msup><ec:mo>=</ec:mo><ec:mn>1</ec:mn><ec:mo>/</ec:mo><ec:msup><ec:mn>2</ec:mn><ec:mo>+</ec:mo></ec:msup></ec:math> and <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"><gc:msup><gc:mi>J</gc:mi><gc:mi>P</gc:mi></gc:msup><gc:mo>=</gc:mo><gc:mn>3</gc:mn><gc:mo>/</gc:mo><gc:msup><gc:mn>2</gc:mn><gc:mo>+</gc:mo></gc:msup></gc:math>, respectively. An overall good agreement of the obtained predictions with available experimental data are found.