Reaction,π−+p→e++e−+n, as a Means of Measuring the Electromagnetic Form Factor of the Charged Pion

Abstract

The success of the single pion exchange approximation in explaining the experimental results for the reaction $\ensuremath{\pi}+n\ensuremath{\rightarrow}\ensuremath{\pi}+\ensuremath{\pi}+n$ in the region of the two-pion resonance suggests that the single pion exchange contribution to the reaction $\ensuremath{\pi}+n\ensuremath{\rightarrow}{e}^{+}+{e}^{\ensuremath{-}}+n$ should be dominant for center-of-mass energies of the electron-positron system in the region of this resonance. A measurement of the rate of this reaction in this region should, therefore, provide direct information about the charged-pion electromagnetic form factor in the neighborhood of the two-pion resonance. We have calculated the differential cross section for the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}{e}^{+}+{e}^{\ensuremath{-}}+n$, assuming a counter experiment. Our estimates indicate that counting rates of the order of ten per hour are attainable by accelerators capable of producing negative-pion beams with an average flux of ${10}^{6}$ pions per second.