Is there an isovector companion of the X(2175)?

Abstract

In this letter we study the reaction e^{+}e^{-}\to\phi \pi^0 \eta with the \pi^{0}\eta system in an isoscalar s-wave configuration. We use a formalism recently developed for the study of e^{+}e^{-}\to\phi \pi\pi and e^{+}e^{-}\to\phi K^{+}K^{-}. The obtained cross section is within the reach of present e^{+}e^{-} machines. Measuring this channel would test the absence of an isovector companion of the X(2175) as predicted by the three body approach to this resonance.