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

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