An exclusive measurement of the decay eta --> pi+ pi- gamma has been performed at the WASA facility at COSY. The eta mesons were produced in the fusion reaction pd --> 3He X at a proton beam momentum of 1.7 GeV/c. Efficiency corrected differential distributions have been extracted based on 13340pm140 events after background subtraction. The measured pion angular distribution is consistent with a relative p-wave of the two-pion system, whereas the measured photon energy spectrum was found at variance with the simplest gauge invariant matrix element of eta --> pi+ pi- gamma. A parameterization of the data can be achieved by the additional inclusion of the empirical pion vector form factor multiplied by a first-order polynomial in the squared invariant mass of the pi+ pi- system.
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