Mesons in a Poincare covariant Bethe-Salpeter approach

We develop a covariant approach to describe the low{lying scalar, pseudoscalar, vector and axialvector mesons as quark{antiquark bound states. This approach is based on an eective interaction modeling of the non{ perturbative structure of the gluon propagator that enters the quark Schwinger{Dyson and meson Bethe{Salpeter equations. We consistently treat these integral equations by precisely implementing the quark propagator functions that solve the Schwinger{Dyson equations into the Bethe{Salpeter equations in the relevant kinematical region. We extract the meson masses and compute the pion and kaon decay constants. We obtain a quantitatively correct description for pions, kaons and vector mesons while the calculated spectra of scalar and axialvector mesons indicate that their structure is more complex than being quark{antiquark bound states.