The Reaction $\gamma \gamma \to {\pi }^0{\pi }^0$ in Generalized Chiral Perturbation Theory

Abstract

The cross section for $\gamma \gamma \to {\pi }^0{\pi }^0$ and the pion polarizabilities are computed, within generalized chiral perturbation theory, in the full one loop approximation, {\it i.e.} up to and including order $O(p^5)$. The result depends on the parameter ${\alpha }_{\pi \pi }$ defining the tree level $\pi -\pi$ scattering amplitude and on an additional low energy constant. The latter is shown to be related by an exact sum-rule to the $e^{+}{e}^{-}$ data. The parameter ${\alpha }_{\pi \pi }$ is related to the quark mass ratio $r=m_s/\hat{m}$ via the expansion of pseudoscalar meson masses. The generalized one loop $\gamma \gamma \to {\pi }^0{\pi }^0$ amplitude agrees with the experimental data in the threshold region provided $r=m_s/\hat{m}\text{lapprox}10$. Higher order corrections are estimated comparing our calculation with the dispersive approach.

Comments: 21 pages (plain latex)+1 fig (using feynman.tex)+ 6 figs (ps file appended), IPNO/TH 94-08