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Dai and Pennington have performed a comprehensive analysis of essentially allpion and kaon pair production data from two-photon collisions below 1.5 GeV,including all high statistics results from Belle, as well as the older datafrom Mark II at SLAC, CELLO at DESY, and Crystal Ball at SLAC. Imposing thebasic constraints required by analyticity, unitarity, and crossing symmetry andmaking use of Low's low-energy theorem for QED, they were able to extract thefinal-state, strong-interaction scattering amplitudes for the intermediate $\pi\pi \to \pi \pi$ and $\pi \pi \to K \overline{K}$ reactions in amodel-independent fashion. In addition, they provided good fits to therespective $\gamma \gamma \to \pi \pi$ cross-sections that are known in thelow-energy sector in the restricted angular range, $| \cos \theta | < 0.6 -0.8$. Using the parameters obtained in this fashion, these authors constructedthe $\gamma \gamma \to \pi \pi$ cross-sections integrated over the full angularrange. In the present work, we use a version of chiral perturbation theorydeveloped by Oller and Oset to evaluate the final-state, strong-interactionamplitudes theoretically, and we compare our low-energy QCD-based results withthe amplitudes extracted by Dai and Pennington. We also calculate the $\gamma\gamma \to \pi \pi$ cross-sections (integrated over the full angular range) andcompare them with those obtained by Dai and Pennington. These calculations givea more detailed insight into the fit of chiral perturbation theory, not just tothe measured $\gamma \gamma \to \pi \pi$ cross-sections, as is usuallypresented, but rather to a higher level of detail through the availableanalysis of the experimental data for the underlying final-state,strong-interaction, meson-meson scattering amplitudes $\pi \pi \to \pi \pi$ and$\pi \pi \to K \overline{K}$ themselves. The fits appear to be sensible.

Amplitude determination for $M M \to M M$, $M = \pi, K$ and  cross-sections for $\gamma \gamma \to \pi^+ \pi^-, \pi^0 \pi^0, \pi^0 \eta$  in a chiral model