Mass-Spectroscopy of [$bb][\bar{b}\bar{b}$] and [$bq][\bar{b}\bar{q}$] tetraquark states in a diquark-antidiquark formalism

Abstract

In this article, we utilise the non-relativistic potential model to calculate the mass-spectra of all bottom [$bb][\bar{b}\bar{b}$] and heavy-light bottom [$bq][\bar{b}\bar{q}$] (q=u,d) tetraquark states in diquark-antidiquark approximation. The four-body problem is reduced into two-body problems by numerically solving the $Schr\ddot{o}dinger$ equation using a cornell-inspired potential along with relativistic correction term. The splitting structure of the tetraquark spectrum is described using spin-dependent terms (spin-spin, spin-orbit, and tensor). We have successfully calculated and predicted the masses of bottom mesons, diquarks and tetraquarks. The masses of S and P-wave tetraquark states [$bb][\bar{b}\bar{b}$] and [$bq][\bar{b}\bar{q}$], respectively, are found to be between 18.7-19.4 GeV and 10.4-11.3 GeV, in which the masses of S-wave [$bb][\bar{b}\bar{b}$] states are less than the 2$\eta_{b}$, $\eta_{b}\Upsilon$, and 2$\Upsilon$ threshold. Additionally, we investigated the $Z_b(10610)$ and $Z_ b(10650)$ states in the current model and found that they are 150 MeV below the $BB^{*}$ and $B^{*}B^{*}$ thresholds.