The Reaction ${\hat{I}}^3{\hat{I}}^3\to \ddot{I}{€}^0\ddot{I}{€}^0$ in Generalized Chiral Perturbation Theory

Abstract

The cross section for ${\hat{I}}^3{\hat{I}}^3\to \ddot{I}{€}^0\ddot{I}{€}^0$ 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 $\hat{I}{\pm }_{\ddot{I}€\ddot{I}€}$ defining the tree level $\ddot{I}€-\ddot{I}€$ 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 $\hat{I}{\pm }_{\ddot{I}€\ddot{I}€}$ is related to the quark mass ratio $r=m_s/\hat{m}$ via the expansion of pseudoscalar meson masses. The generalized one loop ${\hat{I}}^3{\hat{I}}^3\to \ddot{I}{€}^0\ddot{I}{€}^0$ amplitude agrees with the experimental data in the threshold region provided $r= {m_s}/{\hat m}\lapprox 10$. Higher order corrections are estimated comparing our calculation with the dispersive approach.

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