Diabatic representation of exotic hadrons in the dynamical diquark model

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\"odinger equations numerically for hidden-charm tetraquarks of both open and closed strangeness to obtain physical mass eigenvalues, and we explore the di-hadron state content and spatial extent of the eigenstates. As an explicit example, $X(3872)$ emerges with a dominant ${D}^{0}{\overline{D}}^{*0}$ 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.