Is the $f_0(600)$ meson a dynamically generated resonance? -- a lesson learned from the O(N) model and beyond

Abstract

O(N) linear $\sigma$ model is solvable in the large $N$ limit and hence provides a useful theoretical laboratory to test various unitarization approximations. We find that the large $N_c$ limit and the $m_{\sigma }\to \infty$ limit do not commute. In order to get the correct large $N_c$ spectrum one has to firstly take the large $N_c$ limit. We argue that the $f_0(600)$ meson may not be described as generated dynamically. On the contrary, it is most appropriately described at the same level as the pions, i.e, both appear explicitly in the effective lagrangian. Actually it is very likely the $\sigma$ meson responsible for the spontaneous chiral symmetry breaking in a lagrangian with linearly realized chiral symmetry.

15 pages, 3 figurs; references added; discussions slightly modified; revised version accepted by IJMPA

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Cited by in corpus (13)

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• On the size of the sigma meson and its nature
• Lattice Study of Low-lying Nonet Scalar Mesons in Quenched Approximation
• On the two-photon decay width of the sigma meson
• Some Remarks on the Pade Unitarization of Low-Energy Amplitudes
• A simple alternative to the Breit-Wigner distribution
• Chiral Nonet Mixing in ${\eta }^{\prime }\to \eta \pi \pi$ Decay
• SUSY with R-symmetry: confronting EW precision observables and LHC constraints
• Revisiting $O(N)$ $\sigma$ model at unphysical pion masses and high temperatures
• On the pole trajectory of the subthreshold negative parity nucleon with varying pion masses
• Light-flavor resonance dynamics in the $U(3)$ chiral theory
• Review on recent progress in the study of the $N^{\ast }(920)$ subthreshold singularity and the $\sigma /f_0(500)$ meson