Study the molecular nature of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>980</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>a</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>980</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> states

Abstract

We investigate the characteristics of $\ensuremath{\sigma}$, ${f}_{0}(980)$, 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 ${a}_{0}(980)$ cannot be reproduced in the $K\overline{K}$ interactions alone with isospin $I=1$ since the potential is too weak. In our results, the states of $\ensuremath{\sigma}$ 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 $\ensuremath{\pi}\ensuremath{\eta}$ components is much important in the coupled channel interactions to dynamically reproduce the ${a}_{0}(980)$ state, which means that ${a}_{0}(980)$ state cannot be a pure $K\overline{K}$ molecular state. We obtain their radii as: $|\sqrt{⟨{r}^{2}⟩}{|}_{{f}_{0}(980)}=1.80\ifmmode\pm\else\textpm\fi{}0.35\text{ }\text{ }\mathrm{fm}$, $|\sqrt{⟨{r}^{2}⟩}{|}_{\ensuremath{\sigma}}=0.68\ifmmode\pm\else\textpm\fi{}0.05\text{ }\text{ }\mathrm{fm}$ and $|\sqrt{⟨{r}^{2}⟩}{|}_{{a}_{0}(980)}=0.94\ifmmode\pm\else\textpm\fi{}0.09\text{ }\text{ }\mathrm{fm}$. Based on our investigation results, we conclude that the ${f}_{0}(980)$ state is mainly a $K\overline{K}$ bound state, the $\ensuremath{\sigma}$ state a resonance of $\ensuremath{\pi}\ensuremath{\pi}$ and the ${a}_{0}(980)$ state a loose $K\overline{K}$ bound state with the significant compositeness of $\ensuremath{\pi}\ensuremath{\eta}$. From the results of the compositeness, they are not pure molecular states and have something nonmolecular components, especially for the $\ensuremath{\sigma}$ state.

Topics & Concepts