Measurement of the Branching Ratio and Form Factor ofKL→μ+μ−γ

We report on the analysis of the rare decay $K_L\to {\mu }^{+}{\mu }^{-}\gamma$ the 1997 data from the KTeV experiment at Fermilab. A total of 9327 candidate events are observed with $2.4\%$ background, representing a factor of 40 increase in statistics over the current world sample. We find that $B(K_L\to {\mu }^{+}{\mu }^{-}\gamma )=(3.62\pm {0.04}_{\mathrm{stat}}\pm {0.08}_{\mathrm{syst}})\times {10}^{-7\mathrm{}}$. The form factor parameter ${\alpha }_{K^{*}}$ is measured to be ${\alpha }_{K^{*}}{=-0.160\mathrm{}}_{-0.028\mathrm{}}^{+0.026\mathrm{}}$. In addition, we make the first measurement of the parameter $\alpha$ from the D’Ambrosio-Isidori-Portolés form factor, finding $\alpha =-1.54\mathrm{}\pm 0.10$. In that model, this $\alpha$ measurement limits the Cabibbo-Kobayashi-Maskawa parameter $\rho >-0.2\mathrm{}$.