Effects of different Form-factors in Meson-Photon-Photon Transitions and the Muon Anomalous Magnetic Moment

The exact form of the form-factor associated with a meson-photon-photon vertex is not known. Different suggestions exist, based on constraints from QCD and on recent experiments. Four different form-factors are studied in this article. We calculate decay rates for the decays $\pi^{0}\to \gamma\gamma$, $\eta\to \gamma e^{+}e^{-}$, $\eta\to \mu^{+}\mu^{-} e^{+}e^{-}$} and $\eta\to e^{+}e^{-} e^{+}e^{-}$ and cross sections for the processes $e^{+}e^{-}\to PS e^{+}e^{-}$, where $PS=\pi^{0}$, $\eta$ or $\eta'$. The results depend on the choice of form-factor and we examine if the differences are large enough to distinguish in upcoming experiments. The dominant part of the light-by-light contribution to the muon anomalous magnetic moment is also calculated. Here the uncertainty around the choice of form-factor implies that it is possible to estimate a smallest error in the theoretical value of this contribution.