Investigation on the stabilities of doubly heavy tetraquark states

In our recent work [S. Noh and W. Park, Nonrelativistic quark model analysis of <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:math>, ], the mass and binding energy of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>T</c:mi><c:mrow><c:mi>c</c:mi><c:mi>c</c:mi></c:mrow></c:msub></c:math> are found to be 3873 MeV and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo>−</e:mo><e:mn>2</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>MeV</e:mi></e:math>, respectively, which align with the observations reported at LHCb [R. Aaij (LHCb Collaboration), Observation of an exotic narrow doubly charmed tetraquark, ]. Based on our latest quark model approach, we extend our search for other potentially stable configurations of doubly heavy tetraquarks using our nonrelativistic quark model described in Noh and Park, [Nonrelativistic quark model analysis of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>T</g:mi><g:mrow><g:mi>c</g:mi><g:mi>c</g:mi></g:mrow></g:msub></g:math>, ]. Our numerical calculations indicate that the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mover accent="true"><i:mi>u</i:mi><i:mo stretchy="false">¯</i:mo></i:mover><i:mover accent="true"><i:mi>s</i:mi><i:mo stretchy="false">¯</i:mo></i:mover><i:mi>c</i:mi><i:mi>b</i:mi></i:math> configuration is deeply bound. However, the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><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:mi>c</o:mi><o:mi>b</o:mi></o:math> configuration with the isospin symmetry in the light quark sector is relatively less bound. In this study, we emphasize a compulsory aspect for requiring a complete set of three-dimensional harmonic oscillator bases through the discussion of the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mover accent="true"><u:mi>u</u:mi><u:mo stretchy="false">¯</u:mo></u:mover><u:mover accent="true"><u:mi>s</u:mi><u:mo stretchy="false">¯</u:mo></u:mover><u:mi>c</u:mi><u:mi>b</u:mi></u:math> configuration and investigate the essential differences between the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mover accent="true"><ab:mi>u</ab:mi><ab:mo stretchy="false">¯</ab:mo></ab:mover><ab:mover accent="true"><ab:mi>s</ab:mi><ab:mo stretchy="false">¯</ab:mo></ab:mover><ab:mi>c</ab:mi><ab:mi>b</ab:mi></ab:math> and <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mover accent="true"><gb:mi>u</gb:mi><gb:mo stretchy="false">¯</gb:mo></gb:mover><gb:mover accent="true"><gb:mi>d</gb:mi><gb:mo stretchy="false">¯</gb:mo></gb:mover><gb:mi>c</gb:mi><gb:mi>b</gb:mi></gb:math> configurations. Published by the American Physical Society 2024