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

TL;DR

This paper develops a chiral SU(3) Lagrangian for D mesons and charmed baryons, deriving 38 sum rules from heavy-quark symmetry and large-N_c analysis that significantly reduce free parameters.

Contribution

It combines heavy-quark symmetry and large-N_c operator analysis to systematically constrain the two-body counterterms in the chiral Lagrangian involving D mesons and charmed baryons.

Findings

38 independent sum rules reduce free parameters to 4

42 leading two-body counterterms identified

Consistency demonstrated between symmetries and large-N_c analysis

Abstract

We construct, in the work, 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 counter-terms 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 ones at the next-to leading order of $1/N_c$ 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 down to 4 only. This is a remarkable result demonstrating the consistency of the heavy-quark symmetry and large-$N_c$ operator analysis.