Doubly Heavy Tetraquarks in the Born-Oppenheimer approximation

Tetraquarks <math altimg="si1.svg"><mi>Q</mi><mi>Q</mi><mover accent="true"><mrow><mi>q</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mover accent="true"><mrow><mi>q</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></math> are found to be described remarkably well with the Quantum Chromodynamics version of the Hydrogen bond, as treated with the Born-Oppenheimer approximation. We show the robustness of the method by computing the mass of the observed <math altimg="si193.svg"><msub><mrow><mi mathvariant="script">T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> tetraquark following two different paths. Relying on this, we provide a prediction for the mass of the expected <math altimg="si192.svg"><msub><mrow><mi mathvariant="script">T</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> particle. The average sizes of tetraquarks are estimated to be approximately 3–<math altimg="si195.svg"><mn>5</mn><msup><mrow><mspace width="0.20em"/><mtext>GeV</mtext></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo><mn>1</mn></mrow></msup></math>. As a consequence hyperfine separations are not expected to be sizeable. We discussed possible reasons why LHCb has observed only one state in the <math altimg="si10.svg"><mi>D</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> spectrum.