Couplings between the $rho$ and $D$- and $D^ast$-mesons

We compute couplings between the $rho$-meson and $D$- and $D^ast$-mesons - $D^{(ast)}rho D^{(ast)}$ - that are relevant to phenomenological meson-exchange models used to analyse nucleon-$D$-meson scattering and explore the possibility of exotic charmed nuclei. Our framework is built from elements constrained by Dyson-Schwinger equation studies in QCD, and therefore expresses a consistent, simultaneous description of light- and heavy-quarks and the states they constitute, We find that all interactions, including the three independent $D^{ast} rho ,D^{ast}$ couplings, differ markedly amongst themselves in strength and also in range, as measured by their evolution with $rho$-meson virtuality. As a consequence, it appears that no single coupling strength or parametrization can realistically be employed in the study of interactions between $D^{(ast)}$-mesons and matter.