Spectrum and electromagnetic transitions of bottomonium

TL;DR

This paper models the bottomonium spectrum using a nonrelativistic screened potential, accurately predicting masses and electromagnetic transitions, and explaining previously misunderstood decay processes, aiding future experimental observations.

Contribution

It introduces a nonrelativistic screened potential model with non-perturbative spin-dependent corrections to accurately predict bottomonium properties and electromagnetic transitions.

Findings

Predicted bottomonium masses and splittings agree with experimental data.

Successfully explained EM transitions of $mbda(3S)$ states.

Suggested radiative decay chains for missing bottomonium states.

Abstract

Stimulated by the exciting progress in the observation of new bottomonium states, we study the bottomonium spectrum. To calculate the mass spectrum, we adopt 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 wave functions can be included successfully. Furthermore, we calculate the electromagnetic transitions of the $nS$ ($n\leq 4$), $nP$ ($n\leq 3$), and $nD$ ($n\leq 2$) bottomonium states with a nonrelativistic electromagnetic transition operator widely applied to meson photoproduction reactions. Our predicted masses, hyperfine and fine splittings, electromagnetic transition widths and branching ratios of the bottomonium states are in good agreement with the available experimental data. Especially, the EM transitions of $\Upsilon(3S)\to \chi_{b1,2}(1P)\gamma$, which were not well understood in previous studies, can be reasonably explained by considering the corrections of the spin-dependent interactions to the wave functions. We also discuss the observations of the missing bottomonium states by using radiative transitions. Some important radiative decay chains involving the missing bottomonium states are suggested to be observed. We hope our study can provide some useful references to observe and measure the properties of bottomonium mesons in forthcoming experiments.