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Recently Dai and Pennington have performed a comprehensive analysis ofessentially all pion and kaon pair production data from two-photon collisionsbelow 1.5 GeV, including all high statistics results from Belle, as well as theolder data from Mark II at SLAC, CELLO at DESY, and Crystal Ball at SLAC.Imposing the basic constraints required by analyticity, unitarity, and crossingsymmetry and making use of Low's low energy theorem for QED, they are able toextract the final-state strong-interaction scattering amplitudes for theintermediate pi pi->pi pi and pi pi-> K\bar K reactions in a model-independentfashion. In addition, they provide good fits to the respective gamma gamma-> pipi cross-sections that are known in the low-energy sector in the restrictedangular range, | cos theta|< 0.6-0.8. Using the parameters obtained in thisfashion, these authors contruct the \gamma\gamma->pi pi cross-sectionsintegrated over the full angular range. In this work, we use a version ofchiral perturbation theory developed by Oller and Oset to evaluate thefinal-state strong-interaction amplitudes directly theoretically and we compareour thus obtained low-energy QCD-based results directly with the amplitudesextracted by Dai and Pennington. We also calculate the gamma gamma -> pi picross-sections (integrated over the full angular range) and compare these withthose obtained by Dai and Pennington. This calculation thus gives a moredetailed insight into the fit of chiral perturbation theory, not just to themeasured gamma gamma-> pi pi cross-sections, as is usually presented, butrather to a higher level of detail through the available analysis of theexperimental data for the underlying final-state strong-interaction meson-mesonscattering amplitudes pi pi-> pi pi and pi pi-> K\bar K themselves. The fitsappear to be reasonable over the energy range considered.

Amplitude determination for MM -> MM, M= pi, K and cross-sections for gamma gamma -> pi^+pi^-, pi^0 pi^0 in a chiral model