Charged pion pair production by two photons from a chiral sum rule

The cross-section for a charged pion pair production by two photons is evaluated by using the low energy expression previously obtained from current algebra and PCAC which involves an integral over vector and axial-vector spectral functions. Data on the latter obtained from τ-decay as measured by the ALEPH collaboration is then inserted in the integral which is appropriately modified in order to eliminate contributions near the cut in the duality contour integral. The experimental behavior of the cross-section for γγ → π + π − is well reproduced at low energies.