Structure at 2175 MeV in e(+)e(-)->phi f(0)(980) observed via initial-state radiation

We study the initial-state-radiation processes e(+)e(-)-> K+K-pi(+)pi(-)gamma and e(+)e(-)-> K+K-pi(0)pi(0)gamma using an integrated luminosity of 232 fb(-1) collected at the Upsilon(4S) mass with the BABAR detector at SLAC. Even though these reactions are dominated by intermediate states with excited kaons, we are able to study for the first time the cross section for e(+)e(-)->phi(1020)f(0)(980) as a function of center-of-mass energy. We observe a structure near threshold consistent with a 1(--) resonance with mass m=2.175 +/- 0.010 +/- 0.015 GeV/c(2) and width Gamma=58 +/- 16 +/- 20 MeV. We observe no Y(4260) signal and set a limit of B-Y ->phi pi(+)pi(-)center dot Gamma(Y)(ee)< 0.4 eV (90% confidence level), which excludes some models.