Static and dynamic properties of the pion from continuum
modelling of strong QCD

Abstract

We present nonperturbative numerical solutions for the quark propagator Schwinger-Dyson
equation (SDE) and pseudoscalar meson Bethe-Salpeter equation (BSE) at and beyond the
rainbow-ladder truncation level of this system of equations. We solve this coupled system
of integral equations using a phenomenological model for the dressed gluon propagator in
Landau gauge as input. In the rainbow-ladder truncation scheme, we systematically calculate
static properties of the pion and kaon. After combining the rainbow-ladder truncation for the
SDE-BSE system with the impulse approximation for the pion-photon vertex, we present
numerical results for the pion form factor using the Ball-Chiu and bare vertices for the
nonperturbative quark-photon vertex. We find that the Ball-Chiu vertex satisfies
electromagnetic current conservation automatically, however, this vertex gives a charge
pion radius that is less than its experimental value, leaving room for further improvement.
We go beyond the rainbow-ladder truncation by including pion cloud effects into the quark
propagation, and then all the way up into the pion form factor. Here we find significant
changes for the mass and decay constant of the pion. For the pion form factor, on the other
hand, we find no qualitative changes in the region studied for both vertices.
Nevertheless, more work remains to be done at and beyond the rainbow-ladder truncation in
order to connect the pion form factor to the model-independent perturbative result.