The K^- α scattering length and the reaction dd to α K^+ K^-

We present predictions for the the K^- \alpha scattering length obtained within the framework of the multiple scattering approach. Evaluating the pole position of the K^- \alpha scattering amplitude within the zero range approximation, we find a loosely bound K^- \alpha state with a binding energy of E_R = -2 ... -7 MeV and a width \Gamma_R = 11 ... 18 MeV. We propose to measure the K^- \alpha scattering length through the final state interaction between the \alpha and K^- meson produced in the reaction dd \to \alpha K^+ K^-. It is found that the K^-\alpha invariant mass distribution from this reaction at energies near the threshold provides a new tool to determine the s-wave K^- \alpha scattering length.