  We study the e^{+}e^{-} to phi pi pi reaction for pions in an isoscalar
s-wave which is dominated by loop mechanisms. For kaon loops we start from the
conventional RCHPT, but use the unitarized amplitude for KbarK-pipi scattering
and the full kaon form factor instead of the lowest order terms. We study also
effects of vector mesons using RCHPT supplemented with the conventional
anomalous term for VVP interactions and taking into account the effects of
heavy vector mesons in the K*K transition form factor. We find a peak in the
dipion invariant mass around the f_{0}(980) as in the experiment. Selecting the
phi f_{0}(980) contribution as a function of the e^{+}e^{-} energy we also
reproduce the experimental data except for a narrow peak, yielding support to
the existence of a 1^{--} resonance above the phi f_{0}(980) threshold,
coupling strongly to this state.
