Static Bethe-Salpeter approach to bound states of light scalar mesons

In this article are investigated relativistic bound states of light scalar mesons in the framework of the covariant Bethe-Salpeter equation. To this end, it arrives from the covariant Bethe-Salpeter equation for the q q system, via charge conjugation, the corresponding bound-state equation for the two-quark pair, and formulate for a static harmonic kernel the coupled differential equations for the static Bethe-Salpeter amplitude, which is subsequentially solved numerically for a two-body force consisting of a scalar and a fourth-component vector interactions. It's found that the energy spectrum for the ground and the radially excited state of massless quarks shows striking similarities to the corresponding energy spectrum of two nonrelativistic constituent quarks with masses around 300 MeV and a harmonic strength around 30 MeV/fm2, a parameter set characteristic for nonrelativistic quark models