The Y(4260) as a $J/\psi K \bar{K}$ system

A study of the $J/\psi \pi \pi$ and $J/\psi K \bar{K}$ systems, treating them as coupled channels, has been made by solving the Faddeev equations, with the purpose of investigating the possibility of generation of the $J^{PC} = 1^{--}$, Y(4260) resonance due to the interaction between these three mesons. In order to do this, we start by solving the Bethe-Salpeter equation for the two pseudoscalar and for the vector-pseudocalar meson systems using the amplitudes obtained from the lowest order chiral Lagrangians as potentials. With the $t$-matrices generated from these potentials, which contain the poles of the $\sigma$, $f_{0}(980)$ and $a_{0}(980)$ resonances for the pseudoscalar-pseudoscalar system and the pole of the X(3872), alongwith other new charmed resonant states, for the vector-pseudoscalar system, we solve the Faddeev equations. As a result, we get a peak around 4150 MeV with a width $\sim$ 90 MeV when the invariant mass of the two pseudoscalars is close to that of the $f_0 (980)$.