Low-energy photon-photon collisions to two loops revisited

In view of ongoing experimental activities to determine the pion polarizabilities, we have started to recalculate the available two-loop expressions in the framework of chiral perturbation theory, because they have never been checked before. We make use of the chiral Lagrangian at order p6 now available, and of improved techniques to evaluate the two-loop diagrams. Here, we present the result for the neutral pions. The cross section for the reaction γγ→π0π0 agrees with the earlier calculation within a fraction of a percent. We present analytic results for the dipole and quadrupole polarizabilities, and compare the latter with a recent evaluation from data on γγ→π0π0.