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

TL;DR

This paper develops a three-body $KKar K$ model for the $K(1460)$ resonance using Faddeev equations, accounting for mass differences, Coulomb interactions, and potential variations, to explain the resonance's mass splitting and properties.

Contribution

It introduces a novel three-body model for $K(1460)$ incorporating Coulomb effects and potential differences, providing new insights into the resonance's mass splitting and structure.

Findings

Mass splitting of about 10 MeV due to Coulomb interaction.

Reasonable agreement with experimental $K(1460)$ mass.

Effect of $KK$ repulsion and mass polarization analyzed.

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 $K^0K^0{\bar K}^0$, $K^0K^+K^-$ 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.