Measurement of the decay rate and the parameter $\alpha_{K^{*}}$ of the decay $K_{L} \to \mu \mu \gamma$

The rate of the decay of the neutral K meson into $K_{L}^{0} \to \mu \mu \gamma$ has been measured with the NA48 detector at the CERN SPS. A total of 59 events has been observed with an estimated background of 14 events. The overall Kaon flux was determined to be $1.2 \times 10^{9}$. This observation corresponds to a branching ratio of $(3.4 \pm 0.6_{stat} \pm 0.4_{sys}) \times 10^{-7}$. Using this branching ratio the parameter $\alpha_{K^{*}}$ describing the relative strength of the two contributing amplitudes to this decay, through intermediate pseudoscalar or vectorlike mesons, was measured to be $\alpha_{K^{*}} = -0.04_{-0.21}^{+0.24}$