Three-body model for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>K</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1460</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> resonance
Igor Filikhin, Roman Ya. Kezerashvili, Vladimir Suslov, Sh. M. Tsiklauri, Branislav Vlahović
Abstract
We develop the three-body $KK\overline{K}$ model for the $K(1460)$ resonance based on the Faddeev equations in configuration space. A single-channel approach is utilized that takes into account the difference of masses of neutral and charged kaons. It is demonstrated that the mass splitting of the $K(1460)$ resonance takes a place around 1460 MeV according to ${K}^{0}{K}^{0}{\overline{K}}^{0}$, ${K}^{0}{K}^{+}{K}^{\ensuremath{-}}$ and ${K}^{+}{K}^{0}{\overline{K}}^{0}$, ${K}^{+}{K}^{+}{K}^{\ensuremath{-}}$ neutral and charged particle configurations, respectively. The calculations are performed with two sets of $KK$ and $K\overline{K}$ phenomenological potentials, where strength interactions are considered the same for the isospin singlet and triplet states. We study the effect of repulsion of the $KK$ interaction on the mass of the $KK\overline{K}$ system and evaluate the effect of the mass polarization. The Coulomb interaction for description of the $K(1460)$ resonance is considered for the first time. The mass splitting in the $K(1460)$ resonances is evaluated to be in the range of 10 MeV with taking into account the Coulomb force. The three-body model with the $K\overline{K}$ potential, which has the different strengths of the isospin singlet and triplet interactions and is related to the condition of obtaining a quasibound three-body state is also considered. Our results are in reasonable agreement with the experimental mass of the $K(1460)$ resonance.