Abstract
Partial wave dispersion relations for the processes γ Open image in new window →→γ+ Open image in new window and γ+γ→ Open image in new window + Open image in new window to the ordere2 are derived with the help of the Mandelstam representation. The angular momentum decomposition for both processes is carried out and the analytic properties of the partial wave amplitudes are determined. The absorptive parts of these amplitudes along part of the physical branch cuts are calculated by means of the unitarity condition. For γ+ Open image in new window →γ+ Open image in new window the resulting expressions involve amplitudes for single pion photoproduction; for γ+γ→ Open image in new window + Open image in new window they involve theT=0s-wave pion-pion phase shift and the total cross-section for the process γ+π→π+π. The discontinuities along the unphysical branch cuts are calculated by means of crossing symmetry and of analytic continuation through Legendre polynomials. The limits of convergence of the Legendre expansions are discussed and reasons for the importance of the two-pion exchange contribution in photon-nucleon scattering are presented.
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