Disentangling different structures in heavy-light four-quark states

Abstract

Models proposed to explain recently discovered heavy-light four-quark states already assume certain internal structures, i.e. the (anti)quark constituents are grouped into diquark/antidiquark clusters, heavy-meson/light-meson clusters (hadrocharmonium) or heavy-light meson molecules. We propose and use an approach to four-quark states based on Dyson-Schwinger and Bethe-Salpeter equations that has the potential to discriminate between these models. We study the masses of heavy-light $cq\bar{q}\bar{c}$ and $cc\bar{q}\bar{q}$ four-quark states with $q=u,d,s$ and quantum numbers $I(J^{PC})=0(1^{++}),1(1^{+-}),0(0^{++})$ and $1(0^+),0(1^+),1(1^+)$. We identify the dominant components of the ground states with these quantum numbers and suggest candidates for corresponding experimental states. Most notably, we find strong heavy-light meson-meson and negligible diquark-antidiquark components in all $cq\bar{q}\bar{c}$ states, whereas for $cc\bar{q}\bar{q}$ states diquarks are present. A potential caveat in the $I=0$ channels is the necessary but costly inclusion of $c\bar{c}$ components which is relegated to future work.