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 $(245\,\textrm{MeV})^3$. 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.
Highlights
In functional approaches to QCD, the task of computing quark, gluon, and hadron-correlation functions is formulated in terms of closed coupled diagrammatic relations between them, which must be solved numerically
We present a comprehensive study of the quark sector of 2 þ 1 flavor QCD, based on a self-consistent treatment of the coupled system of Schwinger-Dyson equations for the quark propagator and the full quarkgluon vertex in the one-loop dressed approximation
The components of the quark propagator obtained from our approach are in excellent agreement with the results from SchwingerDyson equations, the functional renormalization group, and lattice QCD simulation, a simple benchmark observable being the chiral condensate in the chiral limit, which is computed as ð245 MeVÞ3
Summary
In functional approaches to QCD, the task of computing quark-, gluon-, and hadron-correlation functions is formulated in terms of closed coupled diagrammatic relations between them, which must be solved numerically. In all these approaches, such as Schwinger-Dyson equations (SDEs), functional renormalization group (fRG), n-particle irreducible methods (nPI), and bound state methods [BetheSalpeter (BS), Faddeev- and higher-order equations], the diagrammatic relations are built out of the propagators of the fundamental and composite QCD fields. Functional approaches allow for an attractively simple and versatile access to the dynamical mechanisms that drive numerous fundamental QCD phenomena. Their flexibility in using as external inputs correlation functions
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
