the nature of the a0(980

Tetraquark bound states in a constituent quark model and the nature of the a 0 (980) and f 0 (980) The pseudoscalar and vector meson ground states and their low-energy excited states have been understood as q ¯ q pairs. However, the structure of the scalar mesons, (J P C = 0 ++), remains controversial nowadays. In the naive quark model, to construct a positive parity state requires a unit of angular momentum in a q ¯ q pair. Apparently, this takes an energy around 1 GeV since similar meson states (1 ++ and 2 ++) lie above 1.2 GeV. However a more complicated structure, like q 2 ¯ q 2 , suggested twenty years ago by Jaffe [1] can couple to 0 ++ without orbital excitation and therefore could be a serious candidate to explain the structure of the lightest scalar mesons. In this work we study tetraquark bound states in the framework of the constituent quark model of Ref. [2], which has been used for the description of non-strange two-and three-baryon systems and later on applied to the hadron spectra. The model is based on the idea that between the scale of chiral symmetry breaking and the confinement scale, QCD may be formulated for the light quark sector as an effective theory of constituent quarks interacting through gluon and Goldstone boson exchanges. For the heavy sector chiral symmetry is explicitly broken through the current quark masses and, as a consequence, the interaction reduces to confinement and gluon terms. Expressions of the interaction can be found elsewhere [2]. We will focus in two particular configurations. The first one will be the light-heavy states, [(qq)(¯ Q ¯ Q)], since they are the most prominent candidates to be bound under the strong interaction [3, 4]. The second one will be those tetraquarks with the same quantum numbers as the scalar mesons [5]. We solve the Schrödinger equation using a variational method where the spatial trial wave function is a linear combination of gaussians (1)