Pion photon scattering

Summary  Combining the assumption of a Mandelstam representation with approximate unitarity one can get the pion-photon scattering amplitude in terms of the pion-pion scattering amplitude in even states and of the matrix element forp hotoproduction of pions on pions. In solving this problem attention must be paid to the fact that in the low energy limit this amplitude should become equal to the classical amplitude. With some simplifying assumptions we obtain an expression which contains four quantities: the two pionS-phase shifts, the total cross-section for photoproduction of pions on pions, and the electromagnetic coupling constant. Numerical estimates will be given later. The interest of studying this process lies in its possible influence on the nucleon-photon scattering.