First observation and measurement of the decay $K^{\pm} \to\pi^{\pm}e^{+}e^{-}\gamma$

Using the full data set of the NA48/2 experiment, the decay $K^{\pm} \rightarrow \pi^{\pm} e^{+} e^{-}\gamma$ is observed for the first time, selecting 120 candidates with $7.3 \pm 1.7$ estimated background events. With $K^{\pm} \rightarrow \pi^{\pm} \pi^{0}_{D}$ as normalisation channel, the branching ratio is determined in a model-independent way to be Br$(K^{\pm} \rightarrow \pi^{\pm} e^{+} e^{-}\gamma, m_{ee\gamma} > 260$ MeV/c$^{2}) = (1.19 \pm 0.12_{stat} \pm 0.04_{syst}) \times 10^{-8}$. This measured value and the spectrum of the $e^{+}e^{-}\gamma$ invariant mass allow a comparison with predictions of Chiral Perturbation Theory.