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The chiral SU(3) Lagrangian with pseudoscalar and vector $D$ mesons and withthe octet and decuplet baryons is considered. The leading two-body counterterms involving two baryon fields and two $D$ meson fields are constructed inthe open-charm sector. There are 26 terms. A combined expansion in the inverseof the charm quark mass and in the inverse of the number of colors provides sumrules that reduce the number of free parameter down to 5 only. Our result showsthe feasibility of a systematic computation of the open-charm baryon spectrumbased on coupled-channel dynamics.

Combined large-$N_c$ and heavy-quark operator analysis of 2-body meson-baryon counterterms in the chiral Lagrangian with charmed mesons