Fully coupled functional equations for the quark sector of QCD

Abstract

We present a comprehensive study of the quark sector of $2+1$ flavour QCD, based on a self-consistent treatment of the coupled system of Schwinger-Dyson equations for the quark propagator and the full quark-gluon vertex. The individual form factors of the quark-gluon vertex are expressed in a special tensor basis obtained from a set of gauge-invariant operators. The sole external ingredient used as input to our equations is the Landau gauge gluon propagator with $2+1$ dynamical quark flavours, obtained from studies with Schwinger-Dyson equations, the functional renormalisation group approach, and large volume lattice simulations. The appropriate renormalisation procedure required in order to self-consistently accommodate external inputs stemming from other functional approaches or the lattice is discussed in detail, and the value of the gauge coupling is accurately determined at two vastly separated renormalisation group scales. Our analysis establishes a clear hierarchy among the vertex form factors. We identify only three dominant ones, in agreement with previous results. The components of the quark propagator obtained from our approach are in excellent agreement with the results from Schwinger-Dyson equations, the functional renormalisation group, and lattice QCD simulation, a simple benchmark observable being the chiral condensate in the chiral limit, which is computed as $(245\text{MeV}{)}^3$. The present approach has a wide range of applications, including the self-consistent computation of bound-state properties and finite temperature and density physics, which are briefly discussed.

72 pages, 30 figures. Version including minor changes of version published in PRD. For the benefit of the reader we have also added an Appendix, that contains many more details of the renormalization scheme (MOM${}^2$ scheme) used in this work. In particular we provide a comparison with MOM scheme results in the literature (Appendix A2), as well as the derivation of the RG scheme (Appendix A3)

References in corpus (28)

• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Infrared Properties of QCD from Dyson-Schwinger equations
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Baryons as relativistic three-quark bound states
• Pinch Technique: Theory and Applications
• Chiral symmetry breaking in continuum QCD
• Sketching the Bethe-Salpeter kernel
• Bridging a gap between continuum-QCD and ab initio predictions of hadron observables
• Phase structure of three and four flavor QCD
• Phase diagram and critical endpoint for strongly-interacting quarks
• Dressed-quark anomalous magnetic moments
• The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement
• Scaling behavior and positivity violation of the gluon propagator in full QCD
• On the running coupling constant in QCD
• Nucleon electromagnetic form factors from the covariant Faddeev equation
• Chiral symmetry breaking with lattice propagators
• On the zero crossing of the three-gluon vertex
• Natural constraints on the gluon-quark vertex
• The quark-gluon vertex in Landau gauge bound-state studies
• The strong running coupling from the gauge sector of Domain Wall lattice QCD with physical quark masses
• A Dyson-Schwinger study of the four-gluon vertex
• On light baryons and their excitations
• A new method for determining the quark-gluon vertex
• Further Evidence For Zero Crossing On The Three Gluon Vertex
• Quark-gluon vertex in general kinematics
• Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD
• On non-primitively divergent vertices of Yang-Mills theory
• Precision physics with inclusive QCD processes

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