Heavy baryons in the relativized quark model with chromodynamics

Following the work of Capstick and Isgur [], we systematically study the mass spectrum of the heavy baryons in the relativized quark potential model with chromodynamics. Besides the original Godfrey-Isgur (GI) model, we also adopt a modified GI model which replaces the linear confinement by a screened one. The two models give similar results in our work. All heavy baryons observed so far can be explained as three-quark states. In particular, we identify the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi mathvariant="normal">Ω</a:mi></a:mrow><a:mrow><a:mi>c</a:mi></a:mrow></a:msub><a:mo stretchy="false">(</a:mo><a:mn>3000</a:mn><a:mo stretchy="false">)</a:mo><a:mo>/</a:mo><a:msub><a:mrow><a:mi mathvariant="normal">Ω</a:mi></a:mrow><a:mrow><a:mi>b</a:mi></a:mrow></a:msub><a:mo stretchy="false">(</a:mo><a:mn>6316</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi mathvariant="normal">Ω</i:mi><i:mi>c</i:mi></i:msub><i:mo stretchy="false">(</i:mo><i:mn>3050</i:mn><i:mo stretchy="false">)</i:mo><i:mo>/</i:mo><i:msub><i:mi mathvariant="normal">Ω</i:mi><i:mi>b</i:mi></i:msub><i:mo stretchy="false">(</i:mo><i:mn>6330</i:mn><i:mo stretchy="false">)</i:mo></i:math>, <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 stretchy="false">(</q:mo><q:mn>3065</q:mn><q:mo stretchy="false">)</q:mo><q:mo>/</q:mo><q:msub><q:mi mathvariant="normal">Ω</q:mi><q:mi>b</q:mi></q:msub><q:mo stretchy="false">(</q:mo><q:mn>6340</q:mn><q:mo stretchy="false">)</q:mo></q:math>, and <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>3090</y:mn><y:mo stretchy="false">)</y:mo><y:mo>/</y:mo><y:msub><y:mi mathvariant="normal">Ω</y:mi><y:mi>b</y:mi></y:msub><y:mo stretchy="false">(</y:mo><y:mn>6350</y:mn><y:mo stretchy="false">)</y:mo></y:math> states as the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>p</gb:mi><gb:mi>λ</gb:mi></gb:msub></gb:math> excitations with quantum numbers <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mn>1</ib:mn><ib:mo>/</ib:mo><ib:msup><ib:mn>2</ib:mn><ib:mo>−</ib:mo></ib:msup></ib:math>, <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mn>3</kb:mn><kb:mo>/</kb:mo><kb:msup><kb:mn>2</kb:mn><kb:mo>−</kb:mo></kb:msup></kb:math>, <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mn>3</mb:mn><mb:mo>/</mb:mo><mb:msup><mb:mn>2</mb:mn><mb:mo>−</mb:mo></mb:msup></mb:math>, and <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mn>5</ob:mn><ob:mo>/</ob:mo><ob:msup><ob:mn>2</ob:mn><ob:mo>−</ob:mo></ob:msup></ob:math>. The <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>3120</qb:mn><qb:mo stretchy="false">)</qb:mo></qb:math> is a <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:mn>3</vb:mn><vb:mo>/</vb:mo><vb:msup><vb:mn>2</vb:mn><vb:mo>−</vb:mo></vb:msup></vb:math> state with the <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:msub><xb:mi>p</xb:mi><xb:mi>ρ</xb:mi></xb:msub></xb:math> excitation, whose bottom partner is predicted to be <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:mrow><zb:msub><zb:mrow><zb:mi mathvariant="normal">Ω</zb:mi></zb:mrow><zb:mrow><zb:mi>b</zb:mi></zb:mrow></zb:msub><zb:mo stretchy="false">(</zb:mo><zb:mn>6446</zb:mn><zb:mo>/</zb:mo><zb:mn>6457</zb:mn><zb:mo>,</zb:mo><zb:mn>3</zb:mn><zb:mo>/</zb:mo><zb:msup><zb:mrow><zb:mn>2</zb:mn></zb:mrow><zb:mrow><zb:mo>−</zb:mo></zb:mrow></zb:msup><zb:mo stretchy="false">)</zb:mo></zb:mrow></zb:math>. The higher state <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:msub><ec:mi mathvariant="normal">Ω</ec:mi><ec:mi>c</ec:mi></ec:msub><ec:mo stretchy="false">(</ec:mo><ec:mn>3188</ec:mn><ec:mo stretchy="false">)</ec:mo></ec:math> is the <jc:math xmlns:jc="http://www.w3.org/1998/Math/MathML" display="inline"><jc:mn>2</jc:mn><jc:msub><jc:mi>s</jc:mi><jc:mi>λ</jc:mi></jc:msub></jc:math> excitation with quantum numbers <lc:math xmlns:lc="http://www.w3.org/1998/Math/MathML" display="inline"><lc:mn>1</lc:mn><lc:mo>/</lc:mo><lc:msup><lc:mn>2</lc:mn><lc:mo>+</lc:mo></lc:msup></lc:math>, and <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"><nc:msub><nc:mi mathvariant="normal">Ω</nc:mi><nc:mi>c</nc:mi></nc:msub><nc:mo stretchy="false">(</nc:mo><nc:mn>3327</nc:mn><nc:mo stretchy="false">)</nc:mo></nc:math> is a <sc:math xmlns:sc="http://www.w3.org/1998/Math/MathML" display="inline"><sc:msub><sc:mi>d</sc:mi><sc:mi>λ</sc:mi></sc:msub></sc:math> excitation with quantum numbers <uc:math xmlns:uc="http://www.w3.org/1998/Math/MathML" display="inline"><uc:mn>3</uc:mn><uc:mo>/</uc:mo><uc:msup><uc:mn>2</uc:mn><uc:mo>+</uc:mo></uc:msup></uc:math> or <wc:math xmlns:wc="http://www.w3.org/1998/Math/MathML" display="inline"><wc:mn>5</wc:mn><wc:mo>/</wc:mo><wc:msup><wc:mn>2</wc:mn><wc:mo>+</wc:mo></wc:msup></wc:math>. Published by the American Physical Society 2024