Exclusive measurement of the $\eta \rightarrow \pi^{+} \pi^{-} \gamma$ decay

An exclusive measurement of the decay $\eta \rightarrow \pi^{+} \pi^{-} \gamma$ has been performed at the WASA facility at COSY. The $\eta$ mesons were produced in the fusion reaction $pd \rightarrow ^{3}He X$ at a proton beam momentum of 1.7 GeV/c. Efficiency corrected differential distributions have been extracted based on 13 960 $\pm$ 140 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 $\eta \rightarrow \pi^{+} \pi^{-} \gamma$. 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