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

Abstract

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 ${\eta }^{\prime }$. 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.

Comments: 28p. Master thesis from december 1999 but the results were felt useful for the muon g-2 discussion. Version with more references in preparation