Tetraquarks in the Born-Oppenheimer approximation

TL;DR

This paper refines the theoretical understanding of the $X(3872)$ tetraquark state using an improved Born-Oppenheimer approach, achieving better agreement with experimental data and revealing new insights into its structure.

Contribution

It introduces an improved Born-Oppenheimer model for tetraquarks, providing a more accurate spectrum and decay ratio predictions, and extends the diquark-antidiquark paradigm to include superpositions of open charm states.

Findings

Refined calculation of the decay ratio $ ext{Br}(X o ext{psi}^\prime ext{gamma})/ ext{Br}(X o ext{psi} ext{gamma})$ matches experimental data.

Predicted tetraquark states as compact shallow bound states in color force potentials.

Extended the diquark-antidiquark model to include superpositions of open charm singlets and color octets.

Abstract

The conventional loosely bound molecule interpretation of the $X(3872)$ is not compatible with the recent LHCb experimental measurement of the ratio of branching fractions $\mathcal{R}=\text{Br}(X\to\psi^\prime\gamma)/\text{Br}(X\to\psi\gamma)$. We systematically determine the entire tetraquark spectrum for $J=0,1,2$ and refine the calculation of $\mathcal{R}$ in an improved Born-Oppenheimer description of the $X(3872)$ compact tetraquark. This refinement yields a significantly better agreement with experimental data on ${\cal R}$ and on the spectroscopy of the states themselves. Extending the diquark-antidiquark paradigm to encompass tetraquarks that are linear superposition of open charm singlets and color octets, we discover that these exotic resonances manifest as compact shallow bound states of quarks in color force potentials.