In the framework of the Faddeev equations in configuration space, we investigate the $K$(1460) meson as a resonant state of the $KK\bar{ K}$ kaonic system. We perform calculations for the particle configurations $K^{ 0}K^{ +}K^{ -}$ and $K^{ 0}K^{ +}\overline{ { K}^{ 0}}$ within two models: the $ABC $ model, in which all three particles are distinguishable, and the $AAC$ model when two particles are identical. The models differ in their treatment of the kaon mass difference and the attractive Coulomb force between the $K^{ +}K^{ -}$ pair. We found that the Coulomb shift adds over 1 MeV to the three-body binding energy. The expected correction to the binding energy due to mass redistribution from $AA$ to $AB$ is found to be negligible, up to a maximum of 6\% of the relative mass correction. At the same time, the symmetry of the wave function is distorted depending on the mass ratio value. We found that the repulsive $KK$ interaction plays essential role in the binding energy of the $KK\bar K$ system and report the mass of 1461.8 or 1464.1 MeV for the neutral $K^{ 0}$(1460) and 1466.5 or 1468.8 MeV for the charged $K^{ +}$(1460) resonances, respectively, depending on the parameter sets for $KK$ and $K\bar{ K}$ interactions.
Categories: nucl-th quant-ph