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

We study the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mover accent="true"><a:mi>b</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mover accent="true"><a:mi>b</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mi>u</a:mi><a:mi>d</a:mi></a:math> tetraquark with quantum numbers <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>I</g:mi><g:mo stretchy="false">(</g:mo><g:msup><g:mi>J</g:mi><g:mi>P</g:mi></g:msup><g:mo stretchy="false">)</g:mo><g:mo>=</g:mo><g:mn>0</g:mn><g:mo stretchy="false">(</g:mo><g:msup><g:mn>1</g:mn><g:mo>+</g:mo></g:msup><g:mo stretchy="false">)</g:mo></g:math> as well as the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mover accent="true"><m:mi>b</m:mi><m:mo stretchy="false">¯</m:mo></m:mover><m:mover accent="true"><m:mi>b</m:mi><m:mo stretchy="false">¯</m:mo></m:mover><m:mi>u</m:mi><m:mi>s</m:mi></m:math> tetraquark with quantum numbers <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msup><s:mi>J</s:mi><s:mi>P</s:mi></s:msup><s:mo>=</s:mo><s:msup><s:mn>1</s:mn><s:mo>+</s:mo></s:msup></s:math> using lattice QCD. We improve on existing work by including both local and scattering interpolating operators on both sides of the correlation functions and use symmetric correlation matrices. This allows not only a reliable determination of the energies of QCD-stable tetraquark ground states, but also of low-lying excited states, which are meson-meson scattering states. The latter is particularly important for future finite-volume scattering analyses. Here, we perform chiral and continuum extrapolations of just the ground-state energies, for which finite-volume effects are expected to be small. Our resulting tetraquark binding energies, <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:mo>−</u:mo><u:mn>100</u:mn><u:mo>±</u:mo><u:msubsup><u:mrow><u:mn>10</u:mn></u:mrow><u:mrow><u:mo>−</u:mo><u:mn>51</u:mn></u:mrow><u:mrow><u:mo>+</u:mo><u:mn>36</u:mn></u:mrow></u:msubsup><u:mtext> </u:mtext><u:mtext> </u:mtext><u:mi>MeV</u:mi></u:mrow></u:math> for <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mover accent="true"><w:mi>b</w:mi><w:mo stretchy="false">¯</w:mo></w:mover><w:mover accent="true"><w:mi>b</w:mi><w:mo stretchy="false">¯</w:mo></w:mover><w:mi>u</w:mi><w:mi>d</w:mi></w:math> and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mrow><cb:mo>−</cb:mo><cb:mn>30</cb:mn><cb:mo>±</cb:mo><cb:msubsup><cb:mn>3</cb:mn><cb:mrow><cb:mo>−</cb:mo><cb:mn>31</cb:mn></cb:mrow><cb:mrow><cb:mo>+</cb:mo><cb:mn>11</cb:mn></cb:mrow></cb:msubsup><cb:mtext> </cb:mtext><cb:mtext> </cb:mtext><cb:mi>MeV</cb:mi></cb:mrow></cb:math> for <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mover accent="true"><eb:mi>b</eb:mi><eb:mo stretchy="false">¯</eb:mo></eb:mover><eb:mover accent="true"><eb:mi>b</eb:mi><eb:mo stretchy="false">¯</eb:mo></eb:mover><eb:mi>u</eb:mi><eb:mi>s</eb:mi></eb:math>, are consistent with other recent lattice-QCD predictions. Published by the American Physical Society 2024