  Based on possible albeit tiny, admixtures of mirror matter in ordinary mesons
we study the K_L \to \gamma\gamma transition. We find that this process can be
described with a small SU(3) symmetry breaking of only 3%. We also determine
the eta-eta' mixing angle and the pseudoscalar decay constants. The results for
these parameters are consistent with some obtained in the literature. They
favor two recent determinations; one based on two analytical constraints, and
another one based on next-to-leading order power corrections.
