Three-body model for $K(1460)$ resonance

Abstract

The three-body $KK\bar{K}$ model for the $K(1460)$ resonance is developed on the basis of the Faddeev equations in configuration space. A single-channel approach is using with taking into account the difference of masses of neutral and charged kaons. It is demonstrated that a splitting the mass of the $K(1460)$ resonance takes a place around 1460 MeV according to $K^0{K}^0{\bar{K}}^0$, $K^0{K}^{+}{K}^{-}$ and $K^{+}{K}^0{\bar{K}}^0$, $K^{+}{K}^{+}{K}^{-}$ neutral and charged particle configurations, respectively. The calculations are performed with two sets of $KK$ and $K\bar{K}$ phenomenological potentials, where the latter interaction is considered the same for the isospin singlet and triplet states. The effect of repulsion of the $KK$ interaction on the mass of the $KK\bar{K}$ system is studied and the effect of the mass polarization is evaluated. The first time the Coulomb interaction for description of the $K(1460)$ resonance is considered. The mass splitting in the $K$(1460) resonances is evaluated to be in range of 10 MeV with taking into account the Coulomb force. The three-body model with the $K\bar{K}$ potential, which has the different strength of the isospin singlet and triplet parts that are related by the condition of obtaining a quasi-bound three-body state is also considered. Our results are in reasonable agreement with the experimental mass of the $K(1460)$ resonance.

arXiv comment16 pages 8 figures

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