Steiner tree and exotic multiquarks mesons

We review the long-standing arguments in favor of stable exotic mesons with two heavy quarks and two light antiquarks. For a flavor independent interaction, as suggested by QCD, this mass configuration is favored as compared to equal-mass or hidden-charm configurations, in complete analogy with the pattern observed in atomic physics when the hydrogen molecule is compared to the positronium molecule or to the hydrogen-antihydrogen system.We then present the results of a recent model calculation, inspired by the strong coupling limit of QCD: the linear potential for a quark-antiquark pair in mesons is generalized as a Y-shape interaction for baryons and a Steiner tree for tetraquarks. The four-body problem is then solved by an accurate variational method. An analytic upper bound is also obtained, which confirms the numerical results in the limit of large values for the quark mass ratio.