$D\bar{D}$ interactions are weak near threshold in QCD

TL;DR

This study uses lattice QCD to analyze near-threshold $Dar{D}$ interactions, finding them to be weakly interacting with no evidence of bound states or resonances in the examined energy region.

Contribution

It provides the first lattice QCD analysis of coupled-channel $ ext{eta}_c ext{eta} - Dar{D}$ scattering near threshold, showing weak interactions and no bound states.

Findings

Weakly interacting meson pairs near threshold.

No evidence of bound states or resonances.

Contrasts with previous studies suggesting stronger interactions.

Abstract

We study near-threshold $D\bar{D}$ scattering in $S$ and $D$-wave to determine whether or not resonances or bound states are present. Working in the approximation where charm-annihilation is forbidden, with two degenerate light-quark flavors and a heavier strange quark, isospin is a good quantum number, and the only other other channel that is kinematically open is $\eta_c\eta$. Using lattice QCD we compute, as a function of varying light-quark mass, the $S$-matrix for coupled-channel $\eta_c\eta - D\bar{D}$ scattering and find only weakly interacting meson pairs. In contrast to several other studies, we find no evidence for any bound-state or resonance singularity in the energy region between the deeply-bound $\chi_{c0}(1P)$ state and the $D_s\bar{D}_s$ threshold.