Bottomonium spectrum with a Dirac potential model in the momentum space

Abstract

We study the bottomonium spectrum using a relativistic potential model in the momentum space. This model is based on a complete one gluon exchange interaction with a momentum dependent screening factor to account for the effects due to virtual pair creation that appear close to the decay thresholds. The overall model does not make use of nonrelativistic approximations. We fit well established bottomonium states below the open bottom threshold and predict the rest of the spectrum up to ≈ 11200 MeV and J PC = 3 −−. Uncertainties are treated rigorously and propagated in full to the parameters of the model using a Monte Carlo to identify if which deviations from experimental data can be absorbed into the statistical uncertainties of the models and which can be related to physics beyond the bb picture, guiding future research. We get a good description of the spectrum, in particular the Belle measurement of the η b (2S) state and the Υ (10860) and χ b (3P) resonances.

A local reduction of the Dirac equation applied to the study of quark interactions

“…Moreover, it is possible to introduce into this equation some retardation contributions without formal difficulties. This equation has been used to study the spectra of heavy quarkonia [33,34].…”

Calculation of the One-loop Box Integral at Finite Temperature and Density

“…In that work, two different potentials were considered, with seven and eight free parameters, respectively. The same model was applied to the study of the bottomonium spectrum [13].…”

A relativistic model for the Charmonium spectrum with a reduced number of free parameters

“…In that work two different potentials were considered, with seven and eight free parameters, respectively. The same model was applied to the study of the Bottomonium spectrum [13]. A covariant four-dimensional approach, based on the Schwinger-Dyson equations with a vector contact interaction was used to study the first radial excitations of heavy quarkonium [14].…”