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For the flavor-singlet heavy quark system of bottomonia, we compute themasses of the ground state mesons in four different channels, namely,pseudo-scalar ($\eta_{b}(1S)$), vector ($\Upsilon(1S)$), scalar($\chi_{b_0}(1P)$) and axial vector ($\chi_{b_{1}}(1P)$). We also calculate theweak decay constants of the $\eta_{b}(1S)$ and $\Upsilon(1S)$ as well as thecharge radius of $\eta_{b}(1S)$. It complements our previous study of thecorresponding charmonia systems: $\eta_c(1S)$, $J/\Psi(1S)$, $\chi_{c_0}(1P)$)and ($\chi_{c_{1}}(1P)$). The unified formalism for this analysis is providedby a symmetry-preserving Schwinger-Dyson equations treatment of avector$\times$vector contact interaction. Whenever a comparison is possible,our results are in fairly good agreement with experimental data and modelcalculations based upon Schwinger-Dyson and Bethe-Salpeter equations involvingsophisticated interaction kernels. Within the same framework, we also reportthe elastic and transition form factors to two photons for the pseudo-scalarchannels $\eta_{c}(1S)$ and $\eta_{b}(1S)$ in addition to the elastic formfactors for the vector mesons $J/\Psi$ and $\Upsilon$ for a wide range ofphoton momentum transfer squared ($Q^2$). For $\eta_{c}(1S)$ and$\eta_{b}(1S)$, we also provide predictions of an algebraic model whichcorrelates remarkably well between the known infrared and ultraviolet limits ofthese form factors.

few-body systems

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