Importance of meson-meson and of diquark-antidiquark creation operators for a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mover accent="true"><mml:mi>b</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mover accent="true"><mml:mi>b</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>u</mml:mi><mml:mi>d</mml:mi></mml:math> tetraquark
Pedro Bicudo, Antje Peters, Sebastian Velten, Marc Wagner
Abstract
In recent years, the existence of a hadronically stable $\overline{b}\overline{b}ud$ tetraquark with quantum numbers $I({J}^{P})=0({1}^{+})$ was confirmed by first principles lattice QCD computations. In this work we use lattice QCD to compare two frequently discussed competing structures for this tetraquark by considering meson-meson as well as diquark-antidiquark creation operators. We use the static-light approximation, where the two $\overline{b}$ quarks are assumed to be infinitely heavy with frozen positions, while the light $u$ and $d$ quarks are fully relativistic. By minimizing effective energies and by solving generalized eigenvalue problems we determine the importance of the meson-meson and the diquark-antidiquark creation operators with respect to the ground state. It turns out, that the diquark-antidiquark structure dominates for $\overline{b}\overline{b}$ separations $r\ensuremath{\lesssim}0.25\text{ }\text{ }\mathrm{fm}$, whereas it becomes increasingly more irrelevant for larger separations, where the $I({J}^{P})=0({1}^{+})$ tetraquark is mostly a meson-meson state. We also estimate the meson-meson to diquark-antidiquark ratio of this tetraquark and find around $60%/40%$.