Weak production ofΛparticles near threshold in electron-proton scattering

Abstract

We obtain differential cross sections for the reaction ${e}^{\ensuremath{-}}+\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\Lambda}+{\ensuremath{\nu}}_{e},$ for several incident electron energies near threshold. We are motivated to examine this reaction because it has been proposed as a possible experiment at the Thomas Jefferson National Accelerator Facility to measure the electron neutrino mass. We choose electron energies of 194.25 MeV, 195 MeV, 200 MeV, and 205 MeV so that trends in the cross section may be examined. This calculation is phenomenologically based and makes use of $\mathrm{SU}(3)$ relations, and the form factors so obtained accurately describe $\ensuremath{\Lambda}$ beta decay and so should be correct in this region. We obtain contributions of the individual form factors to the differential cross section and show that the axial vector current form factor increasingly dominates as the electron energy nears threshold. Finally we discuss how the behavior of the cross section in the near threshold region affects its use as a tool to study the electron neutrino mass as has recently been proposed.