String dynamics and metastability of all-heavy tetraquarks

Multiquark states have been advocated to explain recent experimental data in the heavy-light sector, and there are already speculations about multiquarks containing only heavy quarks and antiquarks. With a rigorous treatment of the four-body problem in current quark models, full-charm $(cc\overline{c}\overline{c})$ and full-beauty $(bb\overline{b}\overline{b})$ tetraquarks are found to be unbound. Thus their stability should rely on more subtle effects that are not included in the simple picture of constituent quarks. The case of $(bc\overline{b}\overline{c})$ might be more favorable if the naive color-additive model of confinement is replaced by a string-inspired interaction.

Figure 1

$Y$-shape interaction for the confinement of three quarks.

Figure 2

Double $Y$-shape, or “butterfly” interaction for the confinement of two quarks and two antiquarks.

Figure 3

Flip-flop model for the confinement of two quarks and two antiquarks.