Spin Dependence of Meson Thresholds in the Diabatic Dynamical Diquark Model

TL;DR

The paper tackles the problem of explaining exotic heavy-quark tetraquarks that lie near di-hadron thresholds by extending the dynamical diquark model into a diabatic framework that couples diquark–antidiquark states to di-meson thresholds. It develops HQSS-consistent, spin-dependent diabatic couplings by deriving overlaps and Fierz rearrangements for the diquark sector and by constructing explicit diabatic potential matrices $V^{\eta,J}_{i,i',\ell,\ell'}(r)$ up to total angular momentum $J=2$. The main contributions are the systematic HQSS-based formalism for threshold mixing in the $\delta{\bar{\delta}}$ channel, and the explicit, compact $V$-matrices for all relevant $J^{PC}$ sectors, which are then connected to physical states such as $\chi_{c1}(3872)$ and $T_{c\bar c 1}(3900)$, $T_{c\bar c 1}(4020)$. These results provide a symmetry-constrained, nonperturbative framework to describe near-threshold tetraquarks and offer clear directions for lattice inputs ($h(r)$, $g(r)$) and phenomenological applications.

Abstract

The diabatic dynamical diquark model is designed to unify diquark and molecular approaches for exotic hadrons, by including the effects of di-meson thresholds on fundamental diquark-antidiquark states in order to form physical tetraquarks. We generalize this model by implementing the consequences of heavy-quark spin symmetry for each di-meson pair. We include the specific spin factors and mass differences associated with mesons related by this symmetry (such as $D, D^*$), both features being necessary for the systematic incorporation of effects beyond the static, heavy-source limit inherent to the (adiabatic) Born-Oppenheimer treatment. We obtain explicit interaction potentials for all $J = 0, 1, 2$ states, along the way deriving unusual variants of Fierz reordering identities, and discuss the application of the potentials to specific physical states such as $χ_{c1}(3872)$ and $T_{c\bar c 1}(3900)$.