Charmonia in a Contact Interaction

Abstract

For the flavour-singlet heavy quark system of charmonia, we compute the masses of the ground state mesons in four different channels: pseudo-scalar ($η_c(1S)$), vector ($J/Ψ(1S)$), scalar ($χ_{c_0}(1P)$) and axial vector ($χ_{c_{1}}(1P)$), as well as the weak decay constants of the $η_c(1S)$ and $J/Ψ(1S)$ and the charge radius of $η_c(1S)$. 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 $η_c(1S)$ is consistent with the results from refined SDE studies and lattice Quantum Chromodynamics (QCD).