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.