Study the molecular nature of $\sigma$, $f_0(980)$, and $a_0(980)$ states

Abstract

We investigate the characteristics of $\sigma$, $f_0(980)$, and $a_0(980)$ 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 $a_0(980)$ can not be reproduced in the $K\bar{K}$ interactions with isospin $I=1$ since the potential is too weak. In our results, the states of $\sigma$ and $f_0(980)$ can be dynamically reproduced stably with varying cutoffs both in the coupled channel and the single channel cases. We find that the $\pi \eta$ components is much important in the coupled channel interactions to dynamically reproduce the $a_0(980)$ state, which means that $a_0(980)$ state can not be a pure $K\bar{K}$ molecular state. We obtain their radii as: $|⟨r^2⟩{|}_{f_0(980)}=1.80\pm 0.35$ fm, $|⟨r^2⟩{|}_{\sigma }=0.68\pm 0.05$ fm and $|⟨r^2⟩{|}_{a_0(980)}=0.94\pm 0.09$ fm. Based on our investigation results, we conclude that the $f_0(980)$ state is mainly a $K\bar{K}$ bound state, the $\sigma$ state a resonance of $\pi \pi$ and the $a_0(980)$ state a loose $K\bar{K}$ bound state. From the results of the compositeness, they are not pure molecular states and have something non-molecular components, especially for the $\sigma$ state.

Comments and acknowledgments added

References in corpus (10)

• Multiquark Resonances
• Exotics: Heavy Pentaquarks and Tetraquarks
• Dynamically generated 0^+ heavy mesons in a heavy chiral unitary approach
• Threshold cusps and triangle singularities in hadronic reactions
• Origin of resonances in the chiral unitary approach
• Comprehensive analysis of the wave function of a hadronic resonance and its compositeness
• Couplings in coupled channels versus wave functions in the case of resonances: application to the two $\Lambda (1405)$ states
• Non-ordinary light meson couplings and the $1/N_c$ expansion
• Strong isospin symmetry breaking in light scalar meson production
• Chiral Unitary Dynamics of Hadrons and Hadrons in a Nuclear Medium

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