Abstract
We present non-perturbative first-principle results for quark-, gluon- and meson $1$PI correlation functions of two-flavour Landau-gauge QCD in the vacuum. These correlation functions carry the full information about the theory. They are obtained by solving their Functional Renormalisation Group equations in a systematic vertex expansion, aiming at apparent convergence. This work represents a crucial prerequisite for quantitative first-principle studies of the QCD phase diagram and the hadron spectrum within this framework. In particular, we have computed the gluon, ghost, quark and scalar-pseudoscalar meson propagators, as well as gluon, ghost-gluon, quark-gluon, quark, quark-meson, and meson interactions. 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.
Highlights
Over the past decades, the resolution of the QCD phase structure as well as the hadron spectrum has been at the forefront of research in theoretical hadron physics
In this work we present a self-consistent solution of the system of functional renormalization group (FRG) equations for a large subset of the QCD correlation functions
Note that the dressing functions introduced in (26) are the inverse of the dressing functions Z and G often used in the Dyson-Schwinger equation (DSE) literature to parametrize the gluon and ghost propagators, whereas Zq corresponds to the A function, often used to parametrize the quark propagators; see, e.g., [14,23]
Summary
The resolution of the QCD phase structure as well as the hadron spectrum has been at the forefront of research in theoretical hadron physics. The most important open questions include the existence and location of a critical point in the QCD phase diagram, the spectrum of higher hadronic resonances, and the computation of the dynamical properties of QCD matter from its microscopic description. Answering these qualitative and quantitative questions requires controlled first-principle approaches. Lattice and functional approaches face various conceptual and numerical challenges These range from the sign problem in the former, to the problem of convergent expansion schemes in the latter, and to the need for real-time numerical methods for the dynamics of quantum systems and the hadron spectrum. Complementary and combined studies within different approaches offer important cross-checks, as well as the potential to overcome problems that cannot be addressed within one method alone
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