X(2175) as a resonant state of the $\ddot{I}•K\bar{K}$ system

Abstract

We perform a Faddeev calculation for the three mesons system, $\ddot{I}•K\bar{K}$, taking the interaction between two pseudoscalar mesons and between a vector and a pseudoscalar meson from the chiral unitary approach. We obtain a neat resonance peak around a total mass of 2150 MeV and an invariant mass for the $K\bar{K}$ system around 970 MeV, very close to the $f_0(980)$ mass. The state appears in I=0 and qualifies as a $\ddot{I}•f_0(980)$ resonance. We enlarge the space of states including $\ddot{I}•\ddot{I}€\ddot{I}€$, since $\ddot{I}€\ddot{I}€$ and $K\bar{K}$ build up the $f_0$ (980), and find moderate changes that serve to quantify theoretical uncertainties. No state is seen in I=1. This finding provides a natural explanation for the recent state found at BABAR and BES, the X(2175), which decays into $\ddot{I}•f_0(980)$.

version accepted for publication