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 ($\eta_c(1S)$), vector ($J/\Psi(1S)$), scalar ($\chi_{c_0}(1P)$) and axial vector ($\chi_{c_{1}}(1P)$), as well as the weak decay constants of the $\eta_c(1S)$ and $J/\Psi(1S)$ and the charge radius of $\eta_c(1S)$. The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equation (SDEs) treatment of a vector$\times$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 $\eta_c(1S)$ is consistent with the results from refined SDE studies and lattice Quantum Chromodynamics (QCD). 
Marco A. Bedolla, J.J. Cobos-Mart\'inez, and Adnan Bashir
hep-ph nucl-th