1-20 Bottomonium-like States in Coupled-channel Model with on-shell Approximation

At present the Bottomonium spectra have not been so well explored as the Charmonium spectra. Espescially,the Bottomonium states found in experiment are less than the Charmonium states. However, prior to the discoveryof Zc(3900) in the +J= invariant mass spectra, the charged states possibly composed of at least four-quark is wellestablished in Bottomonium sector, namely the Zb(10610) and Zb(10650) states[1]. They are narrow structures in themass spectra of the ±Υ(nS) (n=1;2;3) and ±hb(mP) (m=1; 2). It is possible to predict other Bottomonium-likestates in the coupled-channel model based on the measured masses and widths of these states. The coupled-channelmodel considers the important rescattering process of final hadrons and is usually proceeded from the Bethe-Salpeterequation, whose expression in the on-shell approximation is written as follows[2]: