Singly heavy omega baryon spectroscopy in the relativistic framework of an independent quark model

The independent quark model, formulated for a three-body system within a relativistic framework, is applied to singly heavy baryons <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> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msubsup><d:mi mathvariant="normal">Ω</d:mi><d:mi>b</d:mi><d:mo>−</d:mo></d:msubsup></d:math> to investigate their spectroscopic properties. A Martin-like potential with an equal mixture of scalar and vector components is employed, with potential parameters fitted using ground-state experimental data. The resulting mass spectra include both radial and orbital excitations. The spin-parity for the recently observed states <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msubsup><g:mi mathvariant="normal">Ω</g:mi><g:mi>c</g:mi><g:mn>0</g:mn></g:msubsup><g:mo stretchy="false">(</g:mo><g:mn>3000</g:mn><g:mo stretchy="false">)</g:mo></g:math>, <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msubsup><l:mi mathvariant="normal">Ω</l:mi><l:mi>c</l:mi><l:mn>0</l:mn></l:msubsup><l:mo stretchy="false">(</l:mo><l:mn>3050</l:mn><l:mo stretchy="false">)</l:mo></l:math>, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msubsup><q:mi mathvariant="normal">Ω</q:mi><q:mi>c</q:mi><q:mn>0</q:mn></q:msubsup><q:mo stretchy="false">(</q:mo><q:mn>3067</q:mn><q:mo stretchy="false">)</q:mo></q:math>, <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:mn>0</v:mn></v:msubsup><v:mo stretchy="false">(</v:mo><v:mn>3120</v:mn><v:mo stretchy="false">)</v:mo></v:math>, and <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msubsup><ab:mi mathvariant="normal">Ω</ab:mi><ab:mi>c</ab:mi><ab:mn>0</ab:mn></ab:msubsup><ab:mo stretchy="false">(</ab:mo><ab:mn>3185</ab:mn><ab:mo stretchy="false">)</ab:mo></ab:math>, as well as possible spin assignments for the four newly observed excited states of <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:msubsup><fb:mi mathvariant="normal">Ω</fb:mi><fb:mi>b</fb:mi><fb:mo>−</fb:mo></fb:msubsup></fb:math> (<ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msubsup><ib:mi mathvariant="normal">Ω</ib:mi><ib:mi>b</ib:mi><ib:mo>−</ib:mo></ib:msubsup><ib:mo stretchy="false">(</ib:mo><ib:mn>6316</ib:mn><ib:mo stretchy="false">)</ib:mo></ib:math>, <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:msubsup><nb:mi mathvariant="normal">Ω</nb:mi><nb:mi>b</nb:mi><nb:mo>−</nb:mo></nb:msubsup><nb:mo stretchy="false">(</nb:mo><nb:mn>6330</nb:mn><nb:mo stretchy="false">)</nb:mo></nb:math>, <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:msubsup><sb:mi mathvariant="normal">Ω</sb:mi><sb:mi>b</sb:mi><sb:mo>−</sb:mo></sb:msubsup><sb:mo stretchy="false">(</sb:mo><sb:mn>6340</sb:mn><sb:mo stretchy="false">)</sb:mo></sb:math>, and <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:msubsup><xb:mi mathvariant="normal">Ω</xb:mi><xb:mi>b</xb:mi><xb:mo>−</xb:mo></xb:msubsup><xb:mo stretchy="false">(</xb:mo><xb:mn>6350</xb:mn><xb:mo stretchy="false">)</xb:mo></xb:math>, are proposed. The magnetic moments of the ground and first excited states are also calculated, along with radiative decay widths and transition magnetic moments. The nonleptonic weak decays of <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:msubsup><cc:mi mathvariant="normal">Ω</cc:mi><cc:mi>c</cc:mi><cc:mn>0</cc:mn></cc:msubsup></cc:math> are analyzed, with decay widths and branching ratios computed and compared with experimental data to validate the predictive power of the model. The branching ratios for the nonleptonic decays of <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"><fc:msubsup><fc:mi mathvariant="normal">Ω</fc:mi><fc:mi>b</fc:mi><fc:mo>−</fc:mo></fc:msubsup></fc:math> are also predicted for future observations.