Light-quark meson description with Schwinger-Dyson equations of quantum chromodynamics

Abstract

One of the greatest contemporary challenges in the study of strongly interactingmatter in the StandardModel of Particle Physics is the understanding of the physical mechanisms behind quark-gluon confinement and hadron formation. The Schwinger-Dyson equations of quantum chromodynamics (QCD) provide a nonperturbative, Poincaré covariant framework to investigate the infrared as well as the ultraviolet behavior of quark and gluon n-point Green functions. They are the basic ingredients in the description of structure properties for hadrons through covariant bound-state equations: the Bethe-Salpeter equation for mesons, and the Faddeev equation for baryons. They comprise an infinite set of coupled integral equations that, for practical purposes, a truncation scheme that preserves local and global symmetries of QCD needs to be specified. In the present project, we aim to investigatelight and heavy-light mesons implementing two different truncation schemes: 1) the decoupling of the gap equation from higher order Green function SDEs by introducing an ansatz for the 3-point quark-gluon vertex, which satisfies the Slavnov-Taylor and transverse Takahashi identities, and an ansatz for the gluon propagator; and 2) use of Dressed Perturbation Theory, which allows for the computation of Green functions as a power series with dressed quark and gluon propagators.