Gernot Eichmann

Nucleon Mass from a Covariant Three-Quark Faddeev Equation

We report the first study of the nucleon where the full Poincaré-covariant structure of the three-quark amplitude is implemented in the Faddeev equation. We employ an interaction kernel which is consistent with contemporary studies of meson properties and aspects of chiral symmetry and its dynamical breaking, thus yielding a comprehensive approach to hadron physics. The resulting current-mass evolution of the nucleon mass compares well with lattice data and deviates only by ∼5% from the quark-diquark result obtained in previous studies.

Toward unifying the description of meson and baryon properties

We present a Poincare covariant Faddeev equation, which enables the simultaneous prediction of meson and baryon observables using the leading order in a truncation of the Dyson-Schwinger equations that can systematically be improved. The solution describes a nucleons dressed-quark core. The evolution of the nucleon mass with current-quark mass is discussed. A nucleon-photon current, which can produce nucleon form factors with realistic Q{sup 2} evolution, is described. Axial-vector diquark correlations lead to a neutron Dirac form factor that is negative, with r{sub 1}{sup nu} > r{sub 1}{sup nd}. The proton electric-magnetic form factor ratio falls with increasing Q{sup 2}.

Nucleon electromagnetic form factors from the covariant Faddeev equation

We compute the electromagnetic form factors of the nucleon in the Poincare-covariant Faddeev framework based on the Dyson-Schwinger equations of QCD. The general expression for a baryons electromagnetic current in terms of three interacting dressed quarks is derived. Upon employing a rainbow-ladder gluon-exchange kernel for the quark-quark interaction, the nucleons Faddeev amplitude and electromagnetic form factors are computed without any further truncations or model assumptions. The form factor results show clear evidence of missing pion-cloud effects below a photon momentum transfer of ~2 GeV^2 and in the chiral region whereas they agree well with experimental data at higher photon momenta. Thus, the approach reflects the properties of the nucleons quark core.

Survey of Nucleon Electromagnetic Form Factors

A dressed-quark core contribution to nucleon electromagnetic form factors is calculated. It is defined by the solution of a Poincaré covariant Faddeev equation in which dressed-quarks provide the elementary degree of freedom and correlations between them are expressed via diquarks. The nucleon-photon vertex involves a single parameter; namely, a diquark charge radius. It is argued to be commensurate with the pion’s charge radius. A comprehensive analysis and explanation of the form factors is built upon this foundation. A particular feature of the study is a separation of form factor contributions into those from different diagram types and correlation sectors, and subsequently a flavour separation for each of these. Amongst the extensive body of results that one could highlight are:

Perspective on rainbow-ladder truncation

{r_1^{n,u} > r_1^{n,d}}

Nucleon to Delta electromagnetic transition in the Dyson-Schwinger approach

, owing to the presence of axial-vector quark-quark correlations; and for both the neutron and proton the ratio of Sachs electric and magnetic form factors possesses a zero.

Tetraquark bound states in a Bethe-Salpeter approach

We present the first Dyson–Schwinger calculation of the three-gluon vertex in Landau-gauge QCD in which its full covariant structure is back-coupled self-consistently. We truncate a Bose-symmetrized version of the Dyson–Schwinger equation at the level of one-loop diagrams, model the four-gluon vertex, and neglect terms that contain nonprimitively divergent n -point functions; the ghost-gluon vertex is taken bare to good approximation. Fit functions for the ghost and gluon propagators that interpolate between scaling and decoupling are presented. In all aspects of our study, Bose symmetry is manifest, from the truncation to the basis decomposition and to the momentum invariants. We explore the uniform and soft-collinear infrared limits and obtain the expected infrared exponents. The presence of a zero crossing in the tree-level component of the vertex is confirmed for both scaling- and decoupling-type scenarios. The zero crossing appears at a scale ∼ 1 GeV ; however, its location might be sensitive to the four-gluon vertex and missing components in the Dyson–Schwinger equation.

A covariant view on the nucleons' quark core

Prima facie the systematic implementation of corrections to the rainbow-ladder truncation of QCDs Dyson-Schwinger equations will uniformly reduce in magnitude those calculated mass-dimensioned results for pseudoscalar and vector meson properties that are not tightly constrained by symmetries. The aim and interpretation of studies employing rainbow-ladder truncation are reconsidered in this light.