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Photon-fusion reactions from the chiral Lagrangian with dynamical light vector mesons

We study the reactions $γγ\rightarrow π^0π^0$, $π^+π^-$, $K^0\bar{K}^0$, $K^+K^-$, $ηη$ and $π^0η$ based on a chiral Lagrangian with dynamical light vector mesons as formulated within the hadrogenesis conjecture. At present our chiral Lagrangian contains 5 unknown parameters that are relevant for the photon fusion reactions. They parameterize the strength of interaction terms involving two vector meson fields. These parameters are fitted to photon fusion data $γγ\rightarrow π^0π^0$, $π^+π^-, π^0η$ and to the decay $η\rightarrowπ^0γγ$. In order to derive gauge invariant reaction amplitudes in the resonance region constraints from micro-causality and exact coupled-channel unitarity are used. Our results are in good agreement with the existing experimental data from threshold up to about 0.9 GeV for the two-pion final states. The $a_0$ meson in the $π^0η$ channel is dynamically generated and an accurate reproduction of the $γγ\rightarrow π^0η$ data is achieved up to 1.2 GeV. Based on our parameter sets we predict the $γγ\rightarrow $ $K^0\bar{K}^0$, $K^+K^-$, $ηη$ cross sections.