Scalar mesons as a mixing of two and four quark states

The scalar mesons are a puzzling problem in meson spectroscopy: they appear to be too numerous and with a mass often incompatible with usual quark-quark potentials. In this paper, we study the possibility to describe them as a mixing of states composed of one and two quark-antiquark pairs. A potential containing confinement, gluon exchange and boson exchange, as expected from chiral symmetry, is used in a consistent way to calculate the two and four quark states separately. Then, a coupling between these states is introduced as a constant term depending only on the flavour of the created pair. The description is largely improved. To refine the treatment, a coupling with a glueball is also considered. All the experimental resonances seem to fit correctly in this scheme. (author)