The Baryon-Baryon Interaction in the Large-$N_c$ Limit

TL;DR

This paper investigates the baryon-baryon interaction within the large-$N_c$ framework, analyzing chiral perturbation theory contributions and symmetry breaking effects, leading to simplified low-energy constants and consistent coupling ratios.

Contribution

It provides a large-$N_c$ analysis of baryon-baryon potentials, reducing the number of relevant low-energy constants and confirming the validity of certain coupling ratios.

Findings

Reduction of low-energy constants from fifteen to three.

Validation of $F/D=2/3$ and $C/D=2$ ratios for couplings.

Successful application of large-$N_c$ results to hyperon-nucleon interactions.

Abstract

We analyze the large-$N_c$ structure of the baryon-baryon potential derived in the framework of SU(3) chiral perturbation theory up to next-to-leading order including contact interactions as well as one-meson and two-meson exchange diagrams. Moreover, we assess the impact of SU(3) symmetry breaking from a large-$N_c$ perspective and show that the leading order results can successfully be applied to the hyperon-nucleon potential. Our results include a reduction of the number of relevant low-energy constants of the leading order contact interaction from fifteen to three, and we show that consistency is preserved if the $F/D$ ratio is given by $2/3$ and the $C/D$ ratio for the baryon decuplet-to-octet coupling is given by 2.