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

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

2008-04-08

arxiv.org/abs/0804.1210v1

Nucl.Phys.A809:65-87,2008

Physics

High Energy Physics

High Energy Physics - Phenomenology

29 pages, 8 figures

Scientific paper

10.1016/j.nuclphysa.2008.05.014

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.

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