We report the first observation of e(+)e(-)->rho(+)rho(-), in a data sample of 379 fb(-1) collected with the BABAR detector at the PEP-II e(+)e(-) storage ring at center-of-mass energies near root s=10.58 GeV. We measure a cross section of sigma(e(+)e(-)->rho(+)rho(-))=8.3 +/- 0.7(stat)+/- 0.8(syst) fb within the range of vertical bar cos theta(*)vertical bar < 0.8 and vertical bar cos theta(+/-)vertical bar < 0.85, where theta(*) is the center-of-mass polar angle of the rho(+/-) meson and theta(+/-) are the angles in the rho(+/-) rest frame between the direction of the boost from the laboratory frame and the direction of the pi(+/-). Assuming production through single-photon annihilation, there are three independent helicity amplitudes. We measure the ratios of their squared moduli to be vertical bar F-00 vertical bar(2)vertical bar F-10 vertical bar(2)vertical bar F-11 vertical bar(2)= 0.51 +/- 0.14(stat)+/- 0.07(syst)0.10 +/- 0.04(stat)+/- 0.01(syst)0.04 +/- 0.03(stat)+/- 0.01(syst). The vertical bar F-00 vertical bar(2) result is inconsistent with the prediction of 1.0 made by QCD models with a significance of 3.1 standard deviations including systematic uncertainties.
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