A new determination of the ${\hat{I}}^3\ddot{I}€\to \ddot{I}€\ddot{I}€$ anomalous amplitude via $\ddot{I}{€}^{-}{e}^{-}\to \ddot{I}{€}^{-}{e}^{-}\ddot{I}{€}^0$ data

Abstract

We discuss the reaction $\ddot{I}{€}^{-}{e}^{-}\to \ddot{I}{€}^{-}{e}^{-}\ddot{I}{€}^0$ with the purpose of obtaining information on the ${\hat{I}}^3\ddot{I}€\to \ddot{I}€\ddot{I}€$ anomalous amplitude ${\mathcal{F}}_{3\ddot{I}€}$. We compare a full calculation at $\mathcal{O}(p^6)$ in chiral perturbation theory and various phenomenological predictions with the existing data of Amendolia {\em et al}. By integrating our theory results using Monte Carlo techniques we obtain $\ddot{I}ƒ=2.05$ nb at $\mathcal{O}(p^6)$ and $\ddot{I}ƒ=2.17$ nb after including the dominant electromagnetic correction. Both results are in good agreement with the experimental cross section of $\ddot{I}ƒ=(2.11\pm 0.47)$ nb. On the basis of the ChPT results one would extract from the the experimental cross section as amplitudes ${\mathcal{F}}_{3\ddot{I}€}^{(0)\mathrm{extr}}=(9.9\pm 1.1)$ GeV${}^{-3}$ and ${\mathcal{F}}_{3\ddot{I}€}^{(0)\mathrm{extr}}=(9.6\pm 1.1)$ GeV${}^{-3}$, respectively, which have to be compared with the low-energy theorem ${\mathcal{F}}_{3\ddot{I}€}=e/(4\ddot{I}{€}^2{F}_{\ddot{I}}{€}^3)=9.72{GeV}^{-3}$. We emphasize the need for new data to allow for a comparison of experimental and theoretical distributions and to obtain ${\mathcal{F}}_{3\ddot{I}€}$ with smaller uncertainty.

23 pages, 14 figures, discussion of the ChPT calculation extended