Diabatic Representation of Exotic Hadrons in the Dynamical Diquark Model

TL;DR

This paper extends the Born-Oppenheimer approach to exotic hadrons by applying a diabatic formalism, enabling the study of mixing between multiquark states and di-hadron thresholds, with numerical solutions for hidden-charm tetraquarks.

Contribution

It introduces a diabatic formalism within the dynamical diquark model to analyze mixing effects in exotic hadrons, providing a new method to compute their mass eigenstates and compositions.

Findings

X(3872) has a dominant D0 D*0 component with significant diquark-antidiquark mixing.

The model predicts a multiplet of diquark-based exotic hadrons.

The approach offers insights into the structure and decay properties of exotic states.

Abstract

We apply the diabatic formalism, an extension of the adiabatic approximation inherent to the Born-Oppenheimer (BO) approach of atomic physics, to the problem of mixing between exotic multiquark hadrons and their nearby di-hadron thresholds. The unperturbed BO eigenstates are obtained using the dynamical diquark model, while the diabatic calculation introduces a mixing potential between these states and the threshold states. We solve the resulting coupled Schr\"{o}dinger equations numerically for hidden-charm tetraquarks of both open and closed strangeness to obtain physical mass eigenvalues, and explore the di-hadron state content and spatial extent of the eigenstates. As an explicit example, $X(3872)$ emerges with a dominant $D^0 \bar D^{*0}$ component, but also contains a considerable diquark-antidiquark component that can contribute significantly to its radiative decay widths, and this component also generates a full multiplet of other diquark-based exotic hadrons to be compared with experiment.