First radial excitations of heavy quarkonium in a contact interaction

Abstract

For the flavor-singlet heavy quark systems of quarkonia, we compute the masses of the first radial excitation of mesons in four different channels: pseudo-scalar (${\eta }_{c,b}(2S)$), vector ($\psi (2S),{\rm Y}(2S)$), scalar (${\chi }_{c_0,b_0}(2P)$) and axial vector (${\chi }_{c_1,b_1}(2P)$), as well as the weak decay constants of the ${\eta }_{c,b}(2S)$ and $\psi (2S),{\rm Y}(2S)$. The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equations treatment of a vector$\times$vector contact interaction. The results found for the meson masses are in good agreement experimental data and earlier model calculations based upon Schwinger-Dyson and Bethe-Salpeter equations (BSEs) involving sophisticated interaction kernels.

Comments: 12 pages, 8 figures