Unified spectroscopic study of bottom mesons and doubly bottom baryons using a relativistic flux-tube model

Using the relativistic flux tube model with spin-dependent corrections, we present a unified investigation of the mass spectra for singly bottom mesons (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>B</a:mi></a:mrow></a:math>, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>B</c:mi><c:mi>s</c:mi></c:msub></c:math>) and doubly bottom baryons (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi mathvariant="normal">Ξ</e:mi><e:mrow><e:mi>b</e:mi><e:mi>b</e:mi></e:mrow></e:msub></e:math>, <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi mathvariant="normal">Ω</h:mi><h:mrow><h:mi>b</h:mi><h:mi>b</h:mi></h:mrow></h:msub></h:math>). Within this framework, the calculated masses for established <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>B</k:mi></k:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>B</m:mi><m:mi>s</m:mi></m:msub></m:math> meson states show excellent agreement with experimental data. Leveraging these reliable predictions for low-lying states, we propose spectroscopic assignments for several higher excitations: we identify the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msubsup><o:mi>B</o:mi><o:mi>J</o:mi><o:mo>*</o:mo></o:msubsup><o:mo stretchy="false">(</o:mo><o:mn>5732</o:mn><o:mo stretchy="false">)</o:mo></o:math> resonance as an excellent candidate for the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mn>1</s:mn><s:mi>P</s:mi><s:mo stretchy="false">(</s:mo><s:msup><s:mn>1</s:mn><s:mo>+</s:mo></s:msup><s:mo stretchy="false">)</s:mo></s:math> state; further, we assign the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>B</w:mi><w:mi>J</w:mi></w:msub><w:mo stretchy="false">(</w:mo><w:mn>5840</w:mn><w:mo stretchy="false">)</w:mo></w:math> resonance as the first radial excitation (<ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mn>2</ab:mn><ab:mi>S</ab:mi></ab:math>), and the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi>B</cb:mi><cb:mi>J</cb:mi></cb:msub><cb:mo stretchy="false">(</cb:mo><cb:mn>5970</cb:mn><cb:mo stretchy="false">)</cb:mo></cb:math> resonance as a <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mn>1</gb:mn><gb:mi>D</gb:mi></gb:math>-wave orbital excitation. In the bottom-strange sector, we predict that the recently observed <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi>B</ib:mi><ib:mrow><ib:mi>s</ib:mi><ib:mi>J</ib:mi></ib:mrow></ib:msub><ib:mo stretchy="false">(</ib:mo><ib:mn>6063</ib:mn><ib:mo stretchy="false">)</ib:mo></ib:math> and <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msub><mb:mi>B</mb:mi><mb:mrow><mb:mi>s</mb:mi><mb:mi>J</mb:mi></mb:mrow></mb:msub><mb:mo stretchy="false">(</mb:mo><mb:mn>6114</mb:mn><mb:mo stretchy="false">)</mb:mo></mb:math> resonances belong to the <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mn>1</qb:mn><qb:mi>D</qb:mi></qb:math>-wave multiplet. Extending our model to doubly bottom baryons, we present comprehensive predictions for the spectra of the <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:msub><sb:mi mathvariant="normal">Ξ</sb:mi><sb:mrow><sb:mi>b</sb:mi><sb:mi>b</sb:mi></sb:mrow></sb:msub></sb:math> and <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:msub><vb:mi mathvariant="normal">Ω</vb:mi><vb:mrow><vb:mi>b</vb:mi><vb:mi>b</vb:mi></vb:mrow></vb:msub></vb:math> baryons, identifying their ground and excited states. These theoretical insights serve as valuable benchmarks, offering guidance for future experimental searches targeting yet-to-be-discovered bottom mesons and doubly bottom baryons.