Charmonia in a Contact Interaction
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 (χc0(1P)) and axial vector (χc1(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).