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 charm threshold and predict the rest of the spectrum up to $\approx 11200$ 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 $b\bar{b}$ 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.