Quark-gluon vertex and structure of mesons and diquarks

*REVISED VERSION* Two quark propagators with different analytic structure are employed in on and off mass-shell Bethe-Salpeter type equations for the pion and scalar diquark form-factors. One of the quark propagators has been calculated with the inclusion of a trivial quark-gluon vertex and, as a consequence, contains a complex conjugate pair of logarithmic branch points. The other quark propagator includes a non-trivial vertex ansatz and is entire, with an essential singularity at infinity. The different quark propagators lead to qualitatively different diquark form-factors.