We obtain the leading divergences at two-loop order for the decays K S → γ γ and K S → γ l + l − using only one-loop diagrams. We then find the double chiral logarithmic corrections to the decay branching ratio of K S → γ γ and to the decay rate for K S → γ l + l − . It turns out that these effects are numerically small and therefore make a very small enhancement on the branching ratio and decay rate. We also derive an expression for the corrections of type log μ × LEC. Numerical analysis done for the process K S → γ γ shows that these single logarithmic effects can be sizable but come with opposite signs with respect to the double chiral logarithms.
