Combined heavy-quark symmetry and large-Nc operator analysis for 2-body counterterms in the chiral Lagrangian with D mesons and charmed baryons

In this work we construct a chiral SU(3) Lagrangian with D mesons of spin J(P) = 0(-) and J(P) = 1(-) and charmed baryons of spin J(P) = 1/2(+) and J(P) = 3/2(+). There are 42 leading two-body counterterms involving two charmed baryon fields and two D meson fields in the constructed Lagrangian. The heavy-quark spin symmetry leads to 35 sum rules, while the large-N-c operator analysis predicts 29 at the next-to leading order of the 1/N-c expansion. The combination of the sum rules from both the heavy-quark symmetry and the large-N-c analysis results in 38 independent sum rules, which reduces the number of free parameters in the chiral Lagrangian to only four. This is a remarkable result demonstrating the consistency of the heavy-quark symmetry and large-N-c operator analysis.