A study of $\eta K\bar{K}$ and ${\eta }^{\prime }K\bar{K}$ with the fixed center approximation to Faddeev equations

Abstract

In the present work we investigate the three-body systems of $\eta K\bar{K}$ and ${\eta }^{\prime }K\bar{K}$, by taking the fixed center approximation to Faddeev equations. We find a clear and stable resonance structure around 1490 MeV in the squared $\eta K\bar{K}$ scattering amplitude, which is not sensitive to the renormalization parameters. Conversely, we get only an enhancement effect of the threshold in the ${\eta }^{\prime }K\bar{K}$ amplitude that indicates the difficulty to bind the ${\eta }^{\prime }K\bar{K}$ system as a consequence of a weaker ${\eta }^{\prime }K$ interaction than the $\eta K$ one. We associate the $\eta K\bar{K}$ state found to the $\eta (1475)$.

Comments: with comment on other work. scale in figures modified. arXiv admin note: text overlap with arXiv:1207.4030