η → π0γγ and γγ → π0π0 in O(p6) chiral perturbation theory

η → π0γγ and γγ → π0π0 are considered in O(p6) chiral perturbation theory. In addition to the usual ϱ, ω contributions, there are two O(p6) operators (L6,m) arising from explicit chiral symmetry breaking. Since only one of the two operators contributes to η → π0γγ, the coefficient of this operator (≡ d3) can be determined in two ways: (i) from the measured decay rate of η → π0γγ, and (ii) by assuming the resonance saturations of the low energy coefficients in the O(p6) chiral lagrangian. We find that two methods lead to vastly different values of d3, which would indicate that either the measured decay rate for η → π0γγ is too large by a factor of 2∼3, or the resonance saturation assumptions do not work for d3.