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 (η b (1S)), vector (Υ(1S)), scalar (χ b 0 (1P )) and axial vector (χ b 1 (1P )). We also calculate the weak decay constants of the η b (1S) and Υ(1S) as well as the charge radius of η b (1S). It complements our previous study of the corresponding charmonia systems: ηc(1S), J/Ψ(1S), χc 0 (1P )) and (χc 1 (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 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 ηc(1S) and η b (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 (Q 2 ). For ηc(1S) and η 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.

Distribution amplitudes of heavy mesons and quarkonia on the light front

“…Herein we re-appreciate earlier work on heavy-light mesons and quarkonia [59][60][61][62][63][64][65] within a continuum approach to two-point and four-point functions whose salient features will be summarized in Sect. 2.…”

Masses of light and heavy mesons and baryons: A unified picture

“…Since then it has been used to study a wide range of mesons in light quark sector [21][22][23][24][25]. Its range of applicability was later extended to the study of charmed and bottom mesons [26][27][28][29]. A calculation of the spectrum of strange and nonstrange hadrons with the CI treatment was published in [24].…”

“…Dimensionless coupling constantα =αIRΛ 2 UV , whereαIR = αIR/m 2 g , for the CI, extracted from a best-fit to data, as explained in Ref [28]…”

Heavy-light mesons in a contact interaction

“…Namely, the homogeneous BSE in an explicit J P C channel is [36][37][38], , whereαIR = αIR/m 2 g , for the contact interaction, extracted from a best-fit to data, as explained in Ref. [23]. Fixed parameters are mg = 0.8 GeV and ΛIR = 0.24 GeV.…”

“…In Table I we present the set of parameters used in previous light-mesons and heavy-quarkonia studies [23]. When studying the heavy sector, a change in the model parameters has to be done: an increase in the ultraviolet regulator, and a reduction in the coupling strength [22].…”