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

Abstract

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 ($\Upsilon(1S)$), 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 $\Upsilon(1S)$ as well as the charge radius of $\eta_{b}(1S)$. It complements our previous study of the corresponding charmonia systems: $\eta_c(1S)$, $J/\Psi(1S)$, $\chi_{c_0}(1P)$) 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 $J/\Psi$ and $\Upsilon$ 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.