Heavy quarkonia in a contact interaction and an algebraic model: mass spectrum, decay constants, charge radii and elastic and transition form factors

For the flavor-singlet heavy quark system of bottomonia, we compute the masses of the ground state mesons in four different channels, namely, pseudo-scalar (${\eta }_b(1S)$), vector ($\mathrm{{\rm Y}}(1S)$), scalar (${\chi }_{b_0}(1P)$) and axial vector (${\chi }_{b_1}(1P)$). We also calculate the weak decay constants of the ${\eta }_b(1S)$ and $\mathrm{{\rm Y}}(1S)$ as well as the charge radius of ${\eta }_b(1S)$. It complements our previous study of the corresponding charmonia systems: ${\eta }_c(1S)$, $J\mathrm{/}\mathrm{\Psi }(1S)$, ${\chi }_{c_0}(1P)$) and (${\chi }_{c_1}(1P)$). The unified formalism for this analysis is provided by a symmetry-preserving Schwinger-Dyson equations treatment of a vector$\times$vector contact interaction. Whenever a comparison is possible, our results are in fairly good agreement with experimental data and model calculations based upon Schwinger-Dyson and Bethe-Salpeter equations involving sophisticated interaction kernels. Within the same framework, we also report the elastic and transition form factors to two photons for the pseudo-scalar channels ${\eta }_c(1S)$ and ${\eta }_b(1S)$ in addition to the elastic form factors for the vector mesons $J\mathrm{/}\mathrm{\Psi }$ and $\mathrm{{\rm Y}}$ for a wide range of photon momentum transfer squared ($Q^2$). For ${\eta }_c(1S)$ and ${\eta }_b(1S)$, we also provide predictions of an algebraic model which correlates remarkably well between the known infrared and ultraviolet limits of these form factors.