Production of Single W Bosons in Electron-Positron Colliding Beams

We compute the total cross section and angular and energy distributions of positrons and single $W$ bosons produced in electron-positron colliding beams. The calculation of the total cross section includes all four lowest-order Feynman diagrams contributing to this process. We limit ourselves to center-of-mass energies $E<2{M}_{W}$ (${M}_{W}$=boson mass). In this range we find that the contribution of two of the diagrams is indeed negligible, but the presence of a pole in one of these diagrams invalidates all previous calculations of the total cross section for $E>2{M}_{W}$. Total cross sections are given for three values of the boson's anomalous magnetic moment $\ensuremath{\kappa}$. We find a rather flat energy distribution of outgoing positrons and a slight peak in the high-energy region of the boson energy distribution. The angular distribution of positrons has a very sharp forward peak (in the direction of the initial positrons), while the bosons are distributed mostly in the backward direction.