<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mi>b</mml:mi><mml:mover accent="true"><mml:mi>u</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mover accent="true"><mml:mi>d</mml:mi><mml:mo

We present a lattice QCD investigation of isoscalar tetraquark systems involving bottom quarks with explicit flavor content <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>b</a:mi><a:mi>b</a:mi><a:mover accent="true"><a:mi>u</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mover accent="true"><a:mi>d</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>b</g:mi><g:mi>s</g:mi><g:mover accent="true"><g:mi>u</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mover accent="true"><g:mi>d</g:mi><g:mo stretchy="false">¯</g:mo></g:mover></g:math>. In the doubly bottom sector, the study focuses on axial-vector <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>J</m:mi><m:mi>P</m:mi></m:msup><m:mo>=</m:mo><m:msup><m:mn>1</m:mn><m:mo>+</m:mo></m:msup></m:math> quantum numbers, whereas in the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>b</o:mi><o:mi>s</o:mi><o:mover accent="true"><o:mi>u</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mover accent="true"><o:mi>d</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math> channel, both axial-vector <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msup><u:mi>J</u:mi><u:mi>P</u:mi></u:msup><u:mo>=</u:mo><u:msup><u:mn>1</u:mn><u:mo>+</u:mo></u:msup></u:math> and scalar <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msup><w:mi>J</w:mi><w:mi>P</w:mi></w:msup><w:mo>=</w:mo><w:msup><w:mn>0</w:mn><w:mo>+</w:mo></w:msup></w:math> quantum numbers are investigated in search of signatures for possible tetraquark bound states. The calculations are performed on four ensembles with dynamical quark fields up to the charm quark generated by the MILC Collaboration, with lattice spacings ranging from approximately 0.058 to 0.12 fm, and at different values of the valence light quark mass <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>m</y:mi><y:mrow><y:mi>u</y:mi><y:mo>/</y:mo><y:mi>d</y:mi></y:mrow></y:msub></y:math>, corresponding to pseudoscalar meson masses, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msub><ab:mi>M</ab:mi><ab:mrow><ab:mi>p</ab:mi><ab:mi>s</ab:mi></ab:mrow></ab:msub><ab:mo>=</ab:mo><ab:mn>0.5</ab:mn></ab:math>, 0.6, and 0.7 GeV. The energy eigenvalues in the finite volume are determined by applying a variational procedure to correlation matrices constructed from two-meson interpolating operators and diquark-antidiquark operators. Continuum extrapolated elastic <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>S</cb:mi></cb:math>-wave scattering amplitudes of <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>B</eb:mi><eb:msup><eb:mi>B</eb:mi><eb:mo>*</eb:mo></eb:msup></eb:math>, <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mi>K</gb:mi><gb:msup><gb:mi>B</gb:mi><gb:mo>*</gb:mo></gb:msup></gb:math>, and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>K</ib:mi><ib:mi>B</ib:mi></ib:math> are extracted from the ground-state eigenenergies following a finite-volume analysis Lüscher. The chiral and continuum extrapolated binding energy estimates for the isoscalar axial-vector doubly bottom tetraquark <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:msub><kb:mi>T</kb:mi><kb:mrow><kb:mi>b</kb:mi><kb:mi>b</kb:mi></kb:mrow></kb:msub></kb:math> from the extracted elastic <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mrow><mb:mi>B</mb:mi><mb:msup><mb:mrow><mb:mi>B</mb:mi></mb:mrow><mb:mrow><mb:mo>*</mb:mo></mb:mrow></mb:msup></mb:mrow></mb:math> <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mrow><ob:mi>S</ob:mi></ob:mrow></ob:math>-wave scattering amplitudes is found to be <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mi mathvariant="normal">Δ</qb:mi><qb:msub><qb:mi>E</qb:mi><qb:msub><qb:mi>T</qb:mi><qb:mrow><qb:mi>b</qb:mi><qb:mi>b</qb:mi></qb:mrow></qb:msub></qb:msub><qb:mo stretchy="false">(</qb:mo><qb:msup><qb:mn>1</qb:mn><qb:mo>+</qb:mo></qb:msup><qb:mo stretchy="false">)</qb:mo><qb:mo>=</qb:mo><qb:mo>−</qb:mo><qb:mn>116</qb:mn><qb:msubsup><qb:mo stretchy="false">(</qb:mo><qb:mrow><qb:mo>−</qb:mo><qb:mn>36</qb:mn></qb:mrow><qb:mrow><qb:mo>+</qb:mo><qb:mn>30</qb:mn></qb:mrow></qb:msubsup><qb:mo stretchy="false">)</qb:mo><qb:mtext> </qb:mtext><qb:mtext> </qb:mtext><qb:mi>MeV</qb:mi></qb:math>. In the <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:mi>b</xb:mi><xb:mi>s</xb:mi><xb:mover accent="true"><xb:mi>u</xb:mi><xb:mo stretchy="false">¯</xb:mo></xb:mover><xb:mover accent="true"><xb:mi>d</xb:mi><xb:mo stretchy="false">¯</xb:mo></xb:mover></xb:math> system, no statistically significant deviations were observed in the ground-state energies from the respective elastic threshold energies, leading to no conclusive evidence for any bound states.