We report a proof-of-principle lattice QCD simulation of the electric and magnetic polarizabilities for a neutral pion
in the four-point function method. The results are based on the same quenched Wilson ensembles on a $24^3\times 48$ lattice at $\beta=6.0$ with pion mass from 1100 to 370 MeV previously used for a charged pion.
For electric polarizability, the results are largely consistent with those from the background field method and ChPT.
In contrast, there are significant differences for magnetic polarizability among the four-point function method, the background field method, and ChPT. The situation points to the important role of disconnected diagrams for a neutral pion.
We elucidate a transparent quark decomposition in the four-point function method that can be used to shed light on the issue.