We report the first study of the nucleon where the full Poincar\'e-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 $\sim${}5% from the quark-diquark result obtained in previous studies.

We present the first Dyson\char21{}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\char21{}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 $$\sim${}1\text{ }\text{ }\mathrm{GeV}$; however, its location might be sensitive to the four-gluon vertex and missing components in the Dyson\char21{}Schwinger equation.

We present results for the charged kaon-box contributions to the hadronic light-by-light (HLBL) correction of the muon’s anomalous magnetic moment. To this end we determine the kaon electromagnetic form factor within the functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations and evaluate the kaon-box contribution as defined in the dispersive approach to HLBL. As an update to previous work we also reevaluate the charged pion-box contribution taking effects due to isospin breaking into account. Our results are $a_{\mu }^{{\pi }^{\pm }-\mathrm{box}}=-15.7(2)(3)\times {10}^{-11}$ and $a_{\mu }^{K^{\pm }-\mathrm{box}}=-0.48(2)(4)\times {10}^{-11}$ thus confirming the large suppression of box contributions beyond the leading pion box.

We compute the electromagnetic form factors of the nucleon in the Poincar\'e-covariant Faddeev framework based on the Dyson-Schwinger equations of QCD. The general expression for a baryon's 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 nucleon's 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 $\sim${}2\,\,GeV2 and in the chiral region, whereas they agree well with experimental data at higher photon momenta. Thus, the approach reflects the properties of the nucleon's quark core.