We present a measurement of pi^+pi^-pi^+pi^- photonuclear production in ultra-peripheral Au-Au collisions at sqrt(s_{NN}) = 200 GeV from the STAR experiment. The pi^+pi^-pi^+pi^- final states are observed at low transverse momentum and are accompanied by mutual nuclear excitation of the beam particles. The strong enhancement of the production cross section at low transverse momentum is consistent with coherent photoproduction. The pi^+pi^-pi^+pi^- invariant mass spectrum of the coherent events exhibits a broad peak around 1540 pm 40 MeV/c^2 with a width of 570 pm 60 MeV/c^2, in agreement with the photoproduction data for the rho^0(1700). We do not observe a corresponding peak in the pi^+pi^- final state and measure an upper limit for the ratio of the branching fractions of the rho^0(1700) to pi^+pi^- and pi^+pi^-pi^+pi^- of 2.5 % at 90 % confidence level. The ratio of rho^0(1700) and rho^0(770) coherent production cross sections is measured to be 13.4 pm 0.8 (stat.) pm 4.4 (syst.) %.
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