Bottomonium spectrum in the relativistic flux tube model

TL;DR

This paper systematically investigates the bottomonium spectrum using the relativistic flux tube model, providing new insights into the structure of higher states and predictions for unobserved states, with results consistent with lattice QCD.

Contribution

The study develops a comprehensive relativistic flux tube model for bottomonium, deriving a Chew-Frautschi like formula and incorporating spin interactions to predict the spectrum.

Findings

Established bottomonium states explained by the RFT model

Predicted masses for 1F and 1G states agree with lattice QCD

Identified possible assignments for $mbda(10750)$, $mbda(10860)$, and $mbda(11020)$

Abstract

The bottomonium spectrum is far from being established. The structures of higher vector states, including the $\Upsilon(10580)$, $\Upsilon(10860)$, and $\Upsilon(11020)$ states, are still in dispute. In addition, whether the $\Upsilon(10750)$ signal which was recently observed by the Belle Collaboration is a normal $b\bar{b}$ state or not should be examined. Faced with such a situation, we carried out a systematic investigation of the bottomonium spectrum in the scheme of the relativistic flux tube (RFT) model. A Chew-Frautschi like formula was derived analytically for the spin average mass of bottomonium states. We further incorporated the spin-dependent interactions and obtained a complete bottomonium spectrum. We found that the most established bottomonium states can be explained in the RFT scheme. The $\Upsilon(10750)$, $\Upsilon(10860)$, and $\Upsilon(11020)$ could be predominantly the $3^3D_1$, $5^3S_1$, and $4^3D_1$ states, respectively. Our predicted masses of $1F$ and $1G$ $b\bar{b}$ states are in agreement with the results given by the method of lattice QCD, which can be tested by experiments in future. We also compared the RFT model with the quark potential model in detail. The differences of these two kinds of models were discussed.