On the nature of the $\Lambda(1405)$ and $\Lambda(1670)$ from their $N_c$ behavior in chiral dynamics

TL;DR

This paper investigates how the properties of the $ ext{Lambda}(1405)$ and $ ext{Lambda}(1670)$ resonances change with the number of colors ($N_c$) using chiral dynamics, revealing their dynamical nature and nontrivial flavor structure.

Contribution

It provides a detailed analysis of the $N_c$ dependence of these resonances within the chiral unitary approach, highlighting their dynamical origin and flavor SU(3) representation effects.

Findings

The $ ext{Lambda}(1405)$'s $ar{K}N$ component remains bound at large $N_c$.

The decay width behavior deviates from the typical $qqq$ state counting rule.

The flavor SU(3) representation influences the $N_c$ evolution of the resonances.

Abstract

We study the behavior with the number of colors ($N_c$) of the $\Lambda(1405)$ and $\Lambda(1670)$ resonances obtained dynamically within the chiral unitary approach. The leading order meson-baryon interaction, used as the kernel of the unitarization procedure, manifests a nontrivial $N_c$ dependence of the flavor SU(3) representation for baryons. As a consequence, the SU(3) singlet (or $\bar{K}N$) component of the $\Lambda(1405)$ states remains bound in the large $N_c$ limit, while the other components dissolve into the continuum. Introducing explicit SU(3) breaking, we obtain the $N_c$ dependence of the excitation energy, masses and widths of the physical $\Lambda(1405)$ and $\Lambda(1670)$ resonance. The $N_c$ behavior of the decay width is found to be different from the general counting rule for a $qqq$ state, indicating the dynamical origin of these resonances.