Doubly heavy tetraquarks from lattice QCD: Incorporating diquark-antidiquark operators and the left-hand cut

Lattice studies of the doubly charm tetraquark <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>T</a:mi><a:mrow><a:mi>c</a:mi><a:mi>c</a:mi></a:mrow></a:msub><a:mo>=</a:mo><a:mi>c</a:mi><a:mi>c</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> require the determination of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>D</g:mi><g:msup><g:mi>D</g:mi><g:mo>*</g:mo></g:msup></g:math> scattering amplitude, which most often incorporate only meson-meson interpolators. We additionally incorporate diquark-antidiquark operators and find that these have some impact on certain eigenenergies. This study presents the first extraction of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>D</i:mi><i:msup><i:mi>D</i:mi><i:mo>*</i:mo></i:msup></i:math> scattering amplitude based on the meson-meson as well as diquark antidiquark interpolators. The effect of the additional operators renders slightly smaller values of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi>p</k:mi></k:mrow></k:math> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mi>cot</m:mi><m:msub><m:mrow><m:mi>δ</m:mi></m:mrow><m:mrow><m:mn>0</m:mn></m:mrow></m:msub></m:mrow></m:math> and a <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>T</o:mi><o:mrow><o:mi>c</o:mi><o:mi>c</o:mi></o:mrow></o:msub></o:math> pole slightly closer to the threshold. The scattering amplitude is extracted from eigenenergies by adopting plane-wave and effective-field-theoretic methods, which also incorporate the left-hand cut and address the partial wave mixing. The <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>T</q:mi><q:mrow><q:mi>c</q:mi><q:mi>c</q:mi></q:mrow></q:msub></q:math> is found to be a subthreshold resonance with a pole at <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:msub><s:mrow><s:mi>m</s:mi></s:mrow><s:mrow><s:msub><s:mrow><s:mi>T</s:mi></s:mrow><s:mrow><s:mi>c</s:mi><s:mi>c</s:mi></s:mrow></s:msub></s:mrow></s:msub><s:mo>−</s:mo><s:msub><s:mrow><s:mi>m</s:mi></s:mrow><s:mrow><s:mi>D</s:mi></s:mrow></s:msub><s:mo>−</s:mo><s:msub><s:mrow><s:mi>m</s:mi></s:mrow><s:mrow><s:msup><s:mrow><s:mi>D</s:mi></s:mrow><s:mrow><s:mo>*</s:mo></s:mrow></s:msup></s:mrow></s:msub><s:mo>=</s:mo><s:mo>−</s:mo><s:msubsup><s:mrow><s:mn>5.2</s:mn></s:mrow><s:mrow><s:mo>−</s:mo><s:mn>0.8</s:mn></s:mrow><s:mrow><s:mo>+</s:mo><s:mn>0.7</s:mn></s:mrow></s:msubsup><s:mo>−</s:mo><s:mi>i</s:mi><s:mo>·</s:mo><s:msubsup><s:mrow><s:mn>6.3</s:mn></s:mrow><s:mrow><s:mo>−</s:mo><s:mn>4.8</s:mn></s:mrow><s:mrow><s:mo>+</s:mo><s:mn>2.4</s:mn></s:mrow></s:msubsup><s:mtext> </s:mtext><s:mtext> </s:mtext><s:mi>MeV</s:mi></s:mrow></s:math>, employing coordinated lattice simulations (CLS) ensembles with <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>m</u:mi><u:mi>π</u:mi></u:msub><u:mo>≃</u:mo><u:mn>280</u:mn><u:mtext> </u:mtext><u:mtext> </u:mtext><u:mi>MeV</u:mi></u:math> and the distillation method. A more significant effect of diquark-antidiquark operators on eigen-energies is found for larger heavy quark masses relevant for <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>T</w:mi><w:mrow><w:mi>b</w:mi><w:mi>b</w:mi></w:mrow></w:msub></w:math>. We find that deeply bound <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>T</y:mi><y:mrow><y:mi>b</y:mi><y:mi>b</y:mi></y:mrow></y:msub></y:math> does not emerge when employing only meson-meson operators, where each meson is separately momentum projected, while the deeply bound state emerges after adding local diquark antidiquark operators.