6533b85ffe1ef96bd12c191a

RESEARCH PRODUCT

X(2175)as a resonant state of theϕKK¯system

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We perform a Faddeev calculation for the three-meson system $\ensuremath{\phi}K\overline{K}$, 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 $\ensuremath{\phi}{f}_{0}(980)$ resonance. We enlarge the space of states including $\ensuremath{\phi}\ensuremath{\pi}\ensuremath{\pi}$, since $\ensuremath{\pi}\ensuremath{\pi}$ 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 $\ensuremath{\phi}{f}_{0}(980)$.