The bosonic algebraic approach applied to the $[QQ][\bar{Q}\bar{Q}]$ tetraquarks

TL;DR

This paper calculates the eigenenergies of heavy tetraquarks using an algebraic approach with Bethe ansatz, showing that the method effectively describes their binding energies and compares favorably with existing models.

Contribution

It introduces an extended transitional Hamiltonian approach with Bethe ansatz for calculating tetraquark energies, providing a novel algebraic framework for heavy tetraquark analysis.

Findings

Heavy tetraquarks exhibit sufficient pairing strength for binding.

The rotational and vibrational transitional theory offers a better description than previous models.

Results align well with current experimental and theoretical literature.

Abstract

The exact eigenenergies of the $T_{4c}=[cc][\bar{c}\bar{c}]$, $T_{4b}=[bb][\bar{b}\bar{b}]$, and $T_{2[bc]}=[bc][\bar{b}\bar{c}]$ tetraquarks are calculated within the extended transitional Hamiltonian approach, in which the so-called Bethe \emph{ansatz} within an infinite-dimensional Lie algebra is used. We fit the parameters appearing in the transitional region from phenomenology associated with potential candidates of tetraquarks. The rotation and vibration transitional theory seems to provide a better description of heavy tetraquarks than other attempts within the same formalism. Our results indicate that the pairing strengths are large enough to provide binding; an extended comparison with the current literature is also performed.