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 (ηb(1S)), vector (Υ(1S)), scalar (χb0(1P)) and axial vector (χb1(1P)). We also calculate the weak decay constants of the ηb(1S) and Υ(1S) as well as the charge radius of ηb(1S). It complements our previous study of the corresponding charmonia systems: ηc(1S), J/Ψ(1S), χc0(1P)) and (χc1(1P)). The unified formalism for this analysis is provided by a symmetry-preserving Schwinger–Dyson equations treatment of a vector × 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 ηc(1S) and ηb(1S) in addition to the elastic form factors for the vector mesons J/Ψ and Υ for a wide range of photon momentum transfer squared (Q2). For ηc(1S) and ηb(1S), we also provide predictions of an algebraic model which correlates remarkably well between the known infrared and ultraviolet limits of these form factors.