Hydrogenlike structures in the strong interaction

Heavy flavor hadrons, especially doubly heavy baryons and doubly heavy tetraquarks, have always received extensive attention in theoretical and experimental research. Given the separation of quark masses <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>m</a:mi><a:mi>Q</a:mi></a:msub><a:mo>≫</a:mo><a:msub><a:mi>m</a:mi><a:mi>q</a:mi></a:msub></a:math> (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>Q</c:mi><c:mo>=</c:mo><c:mi>c</c:mi></c:mrow></c:math>, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>b</e:mi></e:mrow></e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>q</g:mi><g:mo>=</g:mo><g:mi>u</g:mi></g:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>d</i:mi></i:mrow></i:math>, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi>s</k:mi></k:mrow></k:math>), this type of heavy flavor hadrons can be well regarded as hydrogenlike structures in the strong interaction. In the theoretical framework of Born-Oppenheimer approximation, we derive the Schrödinger equation for the motion of light quarks in the effective potential field of heavy quarks. Taking proper account of the color-spin hyperfine interaction, we carry out a systematic study on the mass spectra of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>S</m:mi></m:math>-wave doubly heavy baryons and doubly heavy tetraquarks. The model parameters required for the calculation are obtained by fitting conventional hadrons. The investigation on the doubly heavy baryon systems indicates the reliability of our theoretical approach. Our calculation results show that the experimentally discovered <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msubsup><o:mi>T</o:mi><o:mrow><o:mi>c</o:mi><o:mi>c</o:mi></o:mrow><o:mo>+</o:mo></o:msubsup></o:math> is most likely a compact tetraquark <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mo stretchy="false">|</q:mo><q:mo stretchy="false">(</q:mo><q:mi>c</q:mi><q:mi>c</q:mi><q:msubsup><q:mo stretchy="false">)</q:mo><q:mn>0</q:mn><q:mn>6</q:mn></q:msubsup><q:mo stretchy="false">(</q:mo><q:mover accent="true"><q:mi>u</q:mi><q:mo stretchy="false">¯</q:mo></q:mover><q:mover accent="true"><q:mi>d</q:mi><q:mo stretchy="false">¯</q:mo></q:mover><q:msubsup><q:mo stretchy="false">)</q:mo><q:mn>1</q:mn><q:mover accent="true"><q:mn>6</q:mn><q:mo stretchy="false">¯</q:mo></q:mover></q:msubsup><q:mo stretchy="false">⟩</q:mo></q:math> state with quantum numbers <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mo stretchy="false">(</eb:mo><eb:mi>I</eb:mi><eb:mo>,</eb:mo><eb:msup><eb:mi>J</eb:mi><eb:mi>P</eb:mi></eb:msup><eb:mo stretchy="false">)</eb:mo><eb:mo>=</eb:mo><eb:mo stretchy="false">(</eb:mo><eb:mn>0</eb:mn><eb:mo>,</eb:mo><eb:msup><eb:mn>1</eb:mn><eb:mo>+</eb:mo></eb:msup><eb:mo stretchy="false">)</eb:mo></eb:math>. Furthermore, for different quantum number assignments, some stable tetraquark states are found and may be very narrow peaks. The predictions for other heavy flavor hadrons are expected to be confirmed in new theories and future experiments.