Leading chiral logarithms of KS→γγKS→γγ and KS→γl+l−KS→γl+l− at two loops

We obtain the leading divergences at two-loop order for the decays KS→γγKS→γγ and KS→γl+l−KS→γl+l− using only one-loop diagrams. We then find the double chiral logarithmic corrections to the decay branching ratio of KS→γγKS→γγ and to the decay rate for KS→γl+l−KS→γl+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 logμ×LEC. Numerical analysis done for the process KS→γγKS→γγ shows that these single logarithmic effects can be sizable but come with opposite signs with respect to the double chiral logarithms.