Spectroscopy of light-quark mesons and the nature of the long-range<i>q</i>-<i>q</i>¯ interaction

We have investigated several models of q-q\ifmmode\bar\else\textasciimacron\fi{} binding in light-quark mesons using the Bethe-Salpeter (BS) equation in the instantaneous approximation. These were considered with regard to their ability to reproduce three essential features of the light-quark meson spectroscopy: the existence of light pseudo- scalars, the linearity of Regge trajectories, and the smallness of spin-orbit splittings. This study has led us to reject both the hypothesis of a vector and of a scalar confining potential. Moreover, it has been shown that the BS kernel has to contain a chiral-symmetry-breaking part in order to accommodate the observed spin-orbit splittings. This in turn implies that the BS kernel has to depend on the mass (M) of the bound state itself in order to maintain compatibility with the Goldstone theorem. Under these circumstances we were able to produce a model based on a vector confining potential complemented by an M-dependent reversed spin-orbit coupling which satisfies the three requirements mentioned above. In all these considerations the spontaneous breaking of chiral symmetry plays an essential role not only because of its direct implications on the spectrum but also because it determines the kinetic energy and the quark form factors to be used in the BS equation.

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