We perform a Faddeev calculation for the three-meson system $\varphi K\overline{K}$, 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 $K\overline{K}$ system around 970 MeV, very close to the $f_0(980)$ mass. The state appears in $I=0$ and qualifies as a $\varphi f_0(980)$ resonance. We enlarge the space of states including $\varphi \pi \pi$, since $\pi \pi$ and $K\overline{K}$ 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 $\varphi f_0(980)$.

• Received 29 January 2008

DOI:https://doi.org/10.1103/PhysRevD.78.074031