IS THE f0(600) MESON A DYNAMICALLY GENERATED RESONANCE? — A LESSON LEARNED FROM THE O(N) MODEL AND BEYOND

Abstract

O(N) linear σ 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 Nc limit and the mσ→∞ limit do not commute. In order to get the correct large Nc spectrum one has to first take the large Nc limit. We argue that the f0(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 σ meson responsible for the spontaneous chiral symmetry breaking in a Lagrangian with linearly realized chiral symmetry.