Mesons in a Poincaré covariant Bethe-Salpeter approach

We develop a covariant approach to describe the low-lying scalar, pseudoscalar, vector, and axial-vector mesons as quark-antiquark bound states. This approach is based on an effective interaction modeling the nonperturbative 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 axial-vector mesons suggest that their structure is more complex than being quark-antiquark bound states.