We present a quantitative analysis of chiral symmetry breaking in two-flavour
continuum QCD in the quenched limit. The theory is set-up at perturbative
momenta, where asymptotic freedom leads to precise results. The evolution of
QCD towards the hadronic phase is achieved by means of dynamical hadronisation
in the non-perturbative functional renormalisation group approach. We use a
vertex expansion scheme based on gauge-invariant operators and discuss its
convergence properties and the remaining systematic errors. In particular we
present results for the quark propagator, the full tensor structure and
momentum dependence of the quark-gluon vertex, and the four-fermi scatterings.Comment: 18 pages, 7 figures, additional figure, additional reference
We investigate Landau gauge SU (3) Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalisation group. Particular focus is put on the dynamical creation of the gluon mass gap at non-perturbative momenta and the consistent treatment of quadratic divergences. The non-perturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated selfconsistently with the classical action as only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.
We present nonperturbative first-principle results for quark, gluon, and meson 1PI correlation functions of two-flavor Landau-gauge QCD in the vacuum. These correlation functions carry the full information about the theory. They are obtained by solving their functional renormalization 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 semiperturbative regime for describing the phenomena and scales of confinement and spontaneous chiral symmetry breaking without phenomenological input.
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