Meson-Meson Molecular Binding Potentials in the Diabatic Dynamical Diquark Model

TL;DR

This paper extends the diquark model for tetraquarks by incorporating meson-meson potentials using the diabatic formalism, revealing conditions for states matching observed exotic mesons and pure molecular states.

Contribution

It introduces a novel approach combining diabatic formalism with meson-meson potentials to analyze tetraquark states, providing new insights into their structure and mass spectra.

Findings

Identified parameter regions matching $ ext{X}(3872)$ and $ ext{Z}(3900)$ masses.

Discovered conditions for pure meson-meson molecular states.

Showed how state properties vary with potential parameters.

Abstract

Using the diabatic formalism, a rigorous generalization of the Born-Oppenheimer approximation, we study the effects of introducing simple meson-meson molecular potentials to an established diquark model for tetraquark states, and calculate mixed bound states composed of both diquark-antidiquark and meson-meson molecular components. We examine the behavior of properties of the states as one varies the parameters of the di-meson potential, and find that significant regions of parameter space occur in which one may produce mass eigenstates exactly matching the specific examples of $\chi_{c1}(3872)$ and $\chi_{c0}(3915)$. We also find regions in which a pure di-meson molecular state emerges, and study the same state properties in such cases.