Spectrum and electromagnetic transitions of bottomonium

Wei-Jun Deng, Hui Liu, Long-Cheng Gui, Xian-Hui Zhong

Published 2016-07-16Version 1

Stimulated by the recently exciting progress in the observation of new bottomonium states, we study the bottomonium spectrum. To calculate the mass spectrum, we adopted a nonrelativistic screened potential model. The radial Schr\"{o}dinger equation is solved with the three-point difference central method, where the spin-dependent potentials are dealt with non-perturbatively. With this treatment, the corrections of the spin-dependent potentials to the wavefunctions can be included successfully. Furthermore, we have calculated the electromagnetic transitions of the $nS$, $nP$ ($n\leq 3$), and $nD$ ($n\leq 2$) bottomonium states with a nonrelativistic electromagnetic transition operator widely applied to meson photoproduction reactions. Our calculated masses, hyperfine and fine splittings, and electromagnetic transition rates for the bottomonium states are in good agreement with the available experimental data. We hope our study can provide some useful references to determine the properties of the bottomonium states in forthcoming experiments.