Mesons in a Poincare Covariant Bethe-Salpeter Approach

Abstract

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 effective 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 suggest that their structure is more complex than being quark-antiquark bound states.

18 pages LaTeX, 5 figures; some changes in the presentation, new results on axial vector mesons in enlarged mixing scheme; version to be published in Physical Review D