QCD from gluon, quark, and meson correlators

Mario Mitter (Karl-Franzens-Universität Graz)

We present non-perturbative first-principle results for quark-, gluon- and meson 1PI correlation functions of two-flavour Landau-gauge QCD in the vacuum and Yang-Mills theory at finite temperature. They are obtained by solving their Functional Renormalisation Group equations in a systematic vertex expansion, aiming at apparent convergence within a self-consistent approximation scheme. These correlation functions carry the full information about the theory and their connection to physical observables is discussed. The presented calculations represent a crucial prerequisite for quantitative first-principle studies of QCD and its phase diagram within this framework. In particular, we have computed the ghost, quark and scalar-pseudoscalar meson propagators, as well as gluon, ghost-gluon, quark-gluon, quark, quark-meson, and meson interactions and the magnetic and electric components of the gluon propagator, and the three- and four-gluon vertices. Our results stress the crucial importance of the quantitatively correct running of different vertices in the semi-perturbative regime for describing the phenomena and scales of confinement and spontaneous chiral symmetry breaking without phenomenological input. We confront our results for the correlators with lattice simulations and compare our Debye mass to hard thermal loop perturbation theory. Finally, applications to "QCD-enhanced" low-energy effective models of QCD are discussed.