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arXiv · 0804.1210

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

L. Roca·T. Hyodo·D. Jido
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Abstract

We study the behavior with the number of colors ($N_c$) of the $Λ(1405)$ and $Λ(1670)$ 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 $Λ(1405)$ 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 $Λ(1405)$ and $Λ(1670)$ 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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L. Roca, T. Hyodo, D. Jido. 2008-04-08. On the nature of the $Λ(1405)$ and $Λ(1670)$ from their $N_c$ behavior in chiral dynamics. https://doi.org/10.1016/j.nuclphysa.2008.05.014

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