For the flavor-singlet heavy quark system of charmonia, we compute the masses of the ground state mesons in four different channels: pseudoscalar [${\eta }_c(1S)$], vector [$J/\mathrm{\Psi }(1S)$], 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 $J/\mathrm{\Psi }(1S)$ and the charge radius of ${\eta }_c(1S)$. The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equation (SDE) treatment of a $\text{vector}\times \text{vector}$ contact interaction. 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 involving sophisticated interaction kernels. The charge radius of ${\eta }_c(1S)$ is consistent with the results from refined SDE studies and lattice quantum chromodynamics.

• Received 6 July 2015

DOI:https://doi.org/10.1103/PhysRevD.92.054031