Tetraquarks in the Born-Oppenheimer approximation

A bstract The conventional loosely bound molecule interpretation of the X (3872) is not compatible with the recent LHCb experimental measurement of the ratio of branching fractions $$ \mathcal{R} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> </mml:math> = Br( X → ψ ′ γ ) / Br( X → ψγ ). We systematically determine the entire tetraquark spectrum for J = 0 , 1 , 2 and refine the calculation of $$ \mathcal{R} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> </mml:math> in an improved Born-Oppenheimer description of the X (3872) compact tetraquark. This refinement yields a significantly better agreement with experimental data on $$ \mathcal{R} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> </mml:math> and on the spectroscopy of the states themselves. Extending the diquark-antidiquark paradigm to encompass tetraquarks that are linear super-positions of open charm singlets and color octets, we discover that these exotic resonances manifest as compact shallow bound states of quarks in color force potentials.