The quark-gluon vertex and the QCD infrared dynamics

Abstract

The Dyson-Schwinger quark equation is solved for the quark-gluon vertex using the most recent lattice data available in the Landau gauge for the quark, gluon and ghost propagators, the full set of longitudinal tensor structures in the Ball-Chiu vertex, taking into account a recently derived normalisation for a quark-ghost kernel form factors and the gluon contribution for the tree level quark-gluon vertex identified on a recent study of the lattice soft gluon limit. A solution for the inverse problem is computed after the Tikhonov linear regularisation of the integral equation, that implies solving a modified Dyson-Schwinger equation. We get longitudinal form factors that are strongly enhanced at the infrared region, deviate significantly from the tree level results for quark and gluon momentum below 2 GeV and at higher momentum approach their perturbative values. The computed quark-gluon vertex favours kinematical configurations where the quark momentum p and the gluon momentum q are small and parallel. Further, the quark-gluon vertex is dominated by the form factors associated to the tree level vertex γ µ and to the operator 2 p µ + q µ . The higher rank tensor structures provide small contributions to the vertex.

Chiral effective Lagrangian for heavy-light mesons from QCD

“…LECs calculated from lattice fittings given in Ref[26].Correction M (0)(GeV) fπ (GeV) − ψ ψ (GeV 3 )KeV which is consistent to the experimental result.and e iΓ I [B] ≡ F[O]. The details of Fierz reordering and introducing the extended gluon Green functions could be found in Refs…”

“…In Ref. [26], the authors fitted the lattice results (corresponding to M π ¼ 295 MeV) for the quark wave function renormalization Zð−p 2 Þ and the running quark mass Mð−p 2 Þ. These functions are plotted in Fig.…”

“…The lattice fittings of Zð−p 2 Þ and Mð−p 2 Þ given in Ref [26]. and Σð−p 2 Þ (¼ Mð−p 2 Þ) from DSE with Model A and Model B.…”

The soft-gluon limit and the infrared enhancement of the quark-gluon vertex

“…Herein we pursuit the efforts initiated in [3] and developed further in [4,5] that combine results from lattice simulation in the Landau gauge, for the propagators, and the quark gap equation, together with an exact solution of the Slavnov-Taylor identity for the vertex, to get information on the quark-gluon vertex. The exact solution of the Slavnov-Taylor identity for the vertex calls for the quark-ghost kernel, a four point Green function, that is described in terms of four form factors [6], our unknowns.…”

“…The main novelty in the present work is the inclusion of the lattice results for the soft-gluon limit of the quark-gluon vertex, that translate into normalisation conditions for the quark-ghost kernel form factors. In practice, this was achieved by building an ansatz that is inspired on the analysis of the lattice data for the quarkgluon vertex [4] and the gap equation is solved for the form factors, written as Padé approximants. We stress that all other quantities in the gap equation are known from lattice simulations, including the quark propagator in the Landau gauge.…”