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 ($\varUpsilon (1S)$), 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 $\varUpsilon (1S)$ as well as the charge radius of $\eta _{b}(1S)$. It complements our previous study of the corresponding charmonia systems: $\eta _c(1S)$, $J/\varPsi (1S)$, $\chi _{c_0}(1P)$) 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, model calculations based upon Schwinger–Dyson and Bethe–Salpeter equations involving sophisticated interaction kernels as well as Lattice QCD. 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 $J/\varPsi$ and $\varUpsilon$ 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.