Study of the isoscalar scalar <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mi>c</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 stretchy="false">¯</mml:mo></mml:mover></mml:math> tetraquark <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math> with lattice QCD

Abstract

We present a lattice QCD study of the elastic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi></a:math>-wave <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>D</c:mi><c:mover accent="true"><c:mi>B</c:mi><c:mo stretchy="false">¯</c:mo></c:mover></c:math> scattering in search of tetraquark candidates with explicitly exotic flavor content <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>b</g:mi><g:mi>c</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 isospin <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>I</m:mi><m:mo>=</m:mo><m:mn>0</m:mn></m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>J</o:mi><o:mi>P</o:mi></o:msup><o:mo>=</o:mo><o:msup><o:mn>0</o:mn><o:mo>+</o:mo></o:msup></o:math> channel. We use four lattice QCD ensembles with dynamical <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>u</q:mi><q:mo>/</q:mo><q:mi>d</q:mi></q:math>, <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>s</s:mi></s:math>, and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>c</u:mi></u:math> quark fields generated by the MILC collaboration. A nonrelativistic QCD Hamiltonian, including improvement coefficients up to <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi mathvariant="script">O</w:mi><w:mo stretchy="false">(</w:mo><w:msub><w:mi>α</w:mi><w:mi>s</w:mi></w:msub><w:msup><w:mi>v</w:mi><w:mn>4</w:mn></w:msup><w:mo stretchy="false">)</w:mo></w:math>, is utilized for the bottom quarks. For the rest of the valence quarks we employ a relativistic overlap action. Five different valence quark masses are utilized to study the light quark mass dependence of the <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mi>D</bb:mi><bb:mover accent="true"><bb:mi>B</bb:mi><bb:mo stretchy="false">¯</bb:mo></bb:mover></bb:math> scattering amplitude. The finite volume energy spectra are extracted following a variational approach. The elastic <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mi>D</fb:mi><fb:mover accent="true"><fb:mi>B</fb:mi><fb:mo stretchy="false">¯</fb:mo></fb:mover></fb:math> scattering amplitudes are extracted employing Lüscher’s prescription. The light quark mass dependence of the continuum extrapolated amplitudes suggests an attractive interaction between the <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mover accent="true"><jb:mi>B</jb:mi><jb:mo stretchy="false">¯</jb:mo></jb:mover></jb:math> and <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mi>D</nb:mi></nb:math> mesons. At the physical pseudoscalar meson mass (<pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:msub><pb:mi>M</pb:mi><pb:mrow><pb:mi>p</pb:mi><pb:mi>s</pb:mi></pb:mrow></pb:msub><pb:mo>=</pb:mo><pb:msub><pb:mi>M</pb:mi><pb:mi>π</pb:mi></pb:msub></pb:math>) the <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:mi>D</rb:mi><rb:mover accent="true"><rb:mi>B</rb:mi><rb:mo stretchy="false">¯</rb:mo></rb:mover></rb:math> scattering amplitude has a subthreshold pole corresponding to a binding energy of <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:mo>−</vb:mo><vb:mn>39</vb:mn><vb:msubsup><vb:mo stretchy="false">(</vb:mo><vb:mrow><vb:mo>−</vb:mo><vb:mn>6</vb:mn></vb:mrow><vb:mrow><vb:mo>+</vb:mo><vb:mn>4</vb:mn></vb:mrow></vb:msubsup><vb:mo stretchy="false">)</vb:mo><vb:msubsup><vb:mo stretchy="false">(</vb:mo><vb:mrow><vb:mo>−</vb:mo><vb:mn>18</vb:mn></vb:mrow><vb:mrow><vb:mo>+</vb:mo><vb:mn>8</vb:mn></vb:mrow></vb:msubsup><vb:mo stretchy="false">)</vb:mo><vb:mtext> </vb:mtext><vb:mtext> </vb:mtext><vb:mi>MeV</vb:mi></vb:math> with respect to the <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:mi>D</bc:mi><bc:mover accent="true"><bc:mi>B</bc:mi><bc:mo stretchy="false">¯</bc:mo></bc:mover></bc:math> threshold. The critical <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"><fc:msub><fc:mi>M</fc:mi><fc:mrow><fc:mi>p</fc:mi><fc:mi>s</fc:mi></fc:mrow></fc:msub></fc:math> at which the <hc:math xmlns:hc="http://www.w3.org/1998/Math/MathML" display="inline"><hc:mi>D</hc:mi><hc:mover accent="true"><hc:mi>B</hc:mi><hc:mo stretchy="false">¯</hc:mo></hc:mover></hc:math> scattering length diverges and the system becomes unbound corresponds to <lc:math xmlns:lc="http://www.w3.org/1998/Math/MathML" display="inline"><lc:msubsup><lc:mi>M</lc:mi><lc:mrow><lc:mi>p</lc:mi><lc:mi>s</lc:mi></lc:mrow><lc:mo>*</lc:mo></lc:msubsup><lc:mo>=</lc:mo><lc:mn>2.94</lc:mn><lc:mo stretchy="false">(</lc:mo><lc:mn>15</lc:mn><lc:mo stretchy="false">)</lc:mo><lc:mo stretchy="false">(</lc:mo><lc:mn>5</lc:mn><lc:mo stretchy="false">)</lc:mo><lc:mtext> </lc:mtext><lc:mtext> </lc:mtext><lc:mi>GeV</lc:mi></lc:math>. This result can hold significant experimental relevance in the search for a bound scalar <rc:math xmlns:rc="http://www.w3.org/1998/Math/MathML" display="inline"><rc:msub><rc:mi>T</rc:mi><rc:mrow><rc:mi>b</rc:mi><rc:mi>c</rc:mi></rc:mrow></rc:msub></rc:math> tetraquark, which could well be the next “doubly heavy” bound tetraquark to be discovered with only weak decay modes. Published by the American Physical Society 2024

Topics & Concepts