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

TL;DR

This paper constructs and analyzes two-body counterterms in the chiral Lagrangian involving charmed mesons and baryons, using large-$N_c$ and heavy-quark expansions to reduce parameters and enable systematic spectrum calculations.

Contribution

It introduces a combined large-$N_c$ and heavy-quark operator analysis to simplify the chiral Lagrangian with charmed mesons, reducing free parameters significantly.

Findings

26 counterterms identified in the open-charm sector

Sum rules reduce parameters from 26 to 5

Demonstrates feasibility of systematic open-charm baryon spectrum computation

Abstract

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