Study the molecular nature of σ , f0(980 ), and a0(980 ) states

We investigate the characteristics of σ , f₀(980 ) , and a₀(980 ) with the formalism of chiral unitary approach. With the dynamical generation of them, we make a further study of their properties by evaluating the couplings, the compositeness, the wave functions, and the radii. We also research their properties in the single channel interactions, where the a₀(980 ) cannot be reproduced in the K K ¯ interactions alone with isospin I =1 since the potential is too weak. In our results, the states of σ and f₀(980 ) can be dynamically reproduced stably with varying cutoffs both in the coupled channel and the single channel cases. We find that the π η components is much important in the coupled channel interactions to dynamically reproduce the a₀(980 ) state, which means that a₀(980 ) state cannot be a pure K K ¯ molecular state. We obtain their radii as: |√{⟨r²⟩ }|_f0(980)=1.80 ±0.35 fm , |√{⟨r²⟩ }|_σ=0.68 ±0.05 fm and |√{⟨r²⟩ }|a₀₍₉₈₀₎=0.94 ±0.09 fm . Based on our investigation results, we conclude that the f₀(980 ) state is mainly a K K ¯ bound state, the σ state a resonance of π π and the a₀(980 ) state a loose K K ¯ bound state with the significant compositeness of π η . From the results of the compositeness, they are not pure molecular states and have something nonmolecular components, especially for the σ state.