Eur. Phys. J. A (2021) 57: 289
https://doi.org/10.1140/epja/s10050-021-00601-w

Regular Article - Theoretical Physics

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

Department of Physics, Sardar Vallabhbhai National Institute of Technology, 395007, Surat, Gujarat, India

^c raiajayk@gmail.com

Received: 13 July 2021
Accepted: 2 October 2021
Published online: 18 October 2021

Abstract

In this article, we utilise the non-relativistic potential model to calculate the mass-spectra of all bottom [$bb][\overline{b}\overline{b}$] and heavy-light bottom [$bq][\overline{b}\overline{q}$] (q = u,d) tetraquark states in diquark–antidiquark approximation. The four-body problem is reduced into two body problem 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 [$bb][\overline{b}\overline{b}$] and [$bq][\overline{b}\overline{q}$], respectively, are found to be between 18.7–19.4 GeV and 10.4–11.3 GeV, in which the masses of S-wave [$bb][\overline{b}\overline{b}$] states are less than the 2${\eta }_b$, ${\eta }_b\mathrm{{\rm Y}}$, and 2$\mathrm{{\rm Y}}$ threshold. Additionally, we have investigated the $Z_b(10610)$ and $Z_b(10650)$ states in the current model and found that they are 150 MeV below the $B{B}^{\ast }$ and $B^{\ast }{B}^{\ast }$ thresholds.