We project onto the light-front the pion's Poincaré-covariant Bethe-Salpeter wave-function, obtained using two different approximations to the kernels of QCD's Dyson-Schwinger equations. At an hadronic scale both computed results are concave and significantly broader than the asymptotic distribution amplitude, ϕ asy π (x) = 6x(1 − x); e.g., the integral of ϕπ(x)/ϕ asy π (x) is 1.8 using the simplest kernel and 1.5 with the more sophisticated kernel. Independent of the kernels, the emergent phenomenon of dynamical chiral symmetry breaking is responsible for hardening the amplitude.

The γ * γ → π 0 transition form factor, G(Q 2 ), is computed on the entire domain of spacelike momenta using a continuum approach to the two valence-body bound-state problem in relativistic quantum field theory: the result agrees with data obtained by the CELLO, CLEO and Belle Collaborations. The analysis unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA) and elastic electromagnetic form factor, and demonstrates, too, that a fully self-consistent treatment can readily connect a pion PDA that is a broad, concave function at the hadronic scale with the perturbative QCD prediction for the transition form factor in the hard photon limit. The normalisation of that limit is set by the scale of dynamical chiral symmetry breaking, which is a crucial feature of the Standard Model. Understanding of the latter will thus remain incomplete until definitive transition form factor data is available on Q 2 > 10 GeV 2 .

For the flavour-singlet heavy quark system of charmonia, we compute the masses of the ground state mesons in four different channels: pseudo-scalar (ηc(1S)), vector (J/Ψ(1S)), scalar (χc 0 (1P )) and axial vector (χc 1 (1P )), as well as the weak decay constants of the ηc(1S) and J/Ψ(1S) and the charge radius of ηc(1S). The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equation (SDEs) treatment of a vector×vector contact interaction (CI). The results found for the meson masses and the weak decay constants, for the spin-spin combinations studied, are in fairly good agreement with experimental data and earlier model calculations based upon Schwinger-Dyson and Bethe-Salpeter equations (BSEs) involving sophisticated interaction kernels. The charge radius of ηc(1S) is consistent with the results from refined SDE studies and lattice Quantum Chromodynamics (QCD).

We compute the thermomagnetic correction to the quark-gluon vertex in the presence of a weak magnetic field within the hard thermal loop approximation. The vertex satisfies a QED-like Ward identity with the quark self-energy. The only vertex components that get modified are the longitudinal ones. The calculation provides a first principles result for the quark anomalous magnetic moment at high temperature in a weak magnetic field. We extract the effective thermomagnetic quark-gluon coupling and show that this decreases as a function of the field strength. The result supports the idea that the properties of the effective quark-gluon coupling in the presence of a magnetic field are an important ingredient for understanding the inverse magnetic catalysis phenomenon.